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AuthorTitleYearJournal/ProceedingsReftypeDOI/URL
Lenz, R. The Mehler-Fock Transform in Signal Processing 2017 Entropy
Vol. 19(6), pp. 289 
article  
BibTeX:
@article{Lenz2017,
  author = {Lenz, Reiner},
  title = {The Mehler-Fock Transform in Signal Processing},
  journal = {Entropy},
  publisher = {Multidisciplinary Digital Publishing Institute},
  year = {2017},
  volume = {19},
  number = {6},
  pages = {289}
}
Lenz, R. Eye movements and information geometry 2016 J. Opt. Soc. Am. A
Vol. 33(8), pp. 1598-1603 
article DOI URL 
Abstract: The human visual system uses eye movements to gather visual information. They act as visual scanning processes and can roughly be divided into two different types: small movements around fixation points and larger movements between fixation points. The processes are often modeled as random walks, and recent models based on heavy tail distributions, also known as Lev&x00FD; flights, have been used in these investigations. In contrast to these approaches we do not model the stochastic processes, but we will show that the step lengths of the movements between fixation points follow generalized Pareto distributions (GPDs). We will use general arguments from the theory of extreme value statistics to motivate the usage of the GPD and show empirically that the GPDs provide good fits for measured eye tracking data. In the framework of information geometry the GPDs with a common threshold form a two-dimensional Riemann manifold with the Fisher information matrix as a metric. We compute the Fisher information matrix for the GPDs and introduce a feature vector describing a GPD by its parameters and different geometrical properties of its Fisher information matrix. In our statistical analysis we use eye tracker measurements in a database with 15 observers viewing 1003 images under free-viewing conditions. We use Matlab functions with their standard parameter settings and show that a naive Bayes classifier using the eigenvalues of the Fisher information matrix provides a high classification rate identifying the 15 observers in the database.
BibTeX:
@article{Lenz2016a,
  author = {Reiner Lenz},
  title = {Eye movements and information geometry},
  journal = {J. Opt. Soc. Am. A},
  publisher = {OSA},
  year = {2016},
  volume = {33},
  number = {8},
  pages = {1598--1603},
  url = {http://josaa.osa.org/abstract.cfm?URI=josaa-33-8-1598},
  doi = {http://doi.org/10.1364/JOSAA.33.001598}
}
Lenz, R. Siegel Descriptors for Image Processing 2016 IEEE Signal Processing Letters
Vol. 23(5), pp. 625-628 
article DOI  
BibTeX:
@article{Lenz2016,
  author = {R. Lenz},
  title = {Siegel Descriptors for Image Processing},
  journal = {IEEE Signal Processing Letters},
  year = {2016},
  volume = {23},
  number = {5},
  pages = {625--628},
  doi = {http://doi.org/10.1109/LSP.2016.2542850}
}
Oshima, S., Mochizuki, R., Lenz, R. and Chao, J. Modelling, Measuring and Compensating Color Weak Vision 2016 IEEE Transactions on Image Processing
Vol. 25(6), pp. 2587-2600 
article  
BibTeX:
@article{Oshima2016,
  author = {S. Oshima and R. Mochizuki and R. Lenz and J. Chao},
  title = {Modelling, Measuring and Compensating Color Weak Vision},
  journal = {IEEE Transactions on Image Processing},
  year = {2016},
  volume = {25},
  number = {6},
  pages = {2587--2600}
}
Tasaki, H., Lenz, R. and Chao, J. Simplex-Based Dimension Estimation of Topological Manifolds 2016 23rd International Conference on Pattern Recognition (ICPR)  inproceedings  
BibTeX:
@inproceedings{Tasaki2016,
  author = {Hajime Tasaki and Reiner Lenz and Jinhui Chao},
  title = {Simplex-Based Dimension Estimation of Topological Manifolds},
  booktitle = {23rd International Conference on Pattern Recognition (ICPR)},
  year = {2016}
}
Felsberg, M., Öfjäll, K. and Lenz, R. Unbiased decoding of biologically motivated visual feature descriptors 2015 Frontiers in Robotics and AI
Vol. 2(20) 
article DOI URL 
Abstract: Visual feature descriptors are essential elements in most computer and robot vision systems. They typically lead to an abstraction of the input data, images, or video, for further processing, such as clustering and machine learning. In clustering applications, the cluster center represents the prototypical descriptor of the cluster and estimates the corresponding signal value, such as color value or dominating flow orientation, by decoding the prototypical descriptor. Machine learning applications determine the relevance of respective descriptors and a visualization of the corresponding decoded information is very useful for the analysis of the learning algorithm. Thus decoding of feature descriptors is a relevant problem, frequently addressed in recent work. Also, the human brain represents sensorimotor information at a suitable abstraction level through varying activation of neuron populations. In previous work, computational models have been derived that agree with findings of neurophysiological experiments on the representation of visual information by decoding the underlying signals. However, the represented variables have a bias toward centers or boundaries of the tuning curves. Despite the fact that feature descriptors in computer vision are motivated from neuroscience, the respective decoding methods have been derived largely independent. From first principles, we derive unbiased decoding schemes for biologically motivated feature descriptors with a minimum amount of redundancy and suitable invariance properties. These descriptors establish a non-parametric density estimation of the underlying stochastic process with a particular algebraic structure. Based on the resulting algebraic constraints, we show formally how the decoding problem is formulated as an unbiased maximum likelihood estimator and we derive a recurrent inverse diffusion scheme to infer the dominating mode of the distribution. These methods are evaluated in experiments, where stationary points and bias from noisy image data are compared to existing methods.
BibTeX:
@article{Felsberg2015,
  author = {Felsberg, Michael and Öfjäll, Kristoffer and Lenz, Reiner},
  title = {Unbiased decoding of biologically motivated visual feature descriptors},
  journal = {Frontiers in Robotics and AI},
  year = {2015},
  volume = {2},
  number = {20},
  url = {http://www.frontiersin.org/vision_systems_theory,_tools_and_applications/10.3389/frobt.2015.00020/abstract},
  doi = {http://doi.org/10.3389/frobt.2015.00020}
}
Lenz, R. Generalized Pareto Distributions, Image Statistics and Autofocusing in Automated Microscopy 2015
Vol. 9389Geometric Science of Information, pp. 96-103 
incollection DOI URL 
BibTeX:
@incollection{Lenz2015,
  author = {Lenz, Reiner},
  title = {Generalized Pareto Distributions, Image Statistics and Autofocusing in Automated Microscopy},
  booktitle = {Geometric Science of Information},
  publisher = {Springer International Publishing},
  year = {2015},
  volume = {9389},
  pages = {96--103},
  url = {http://dx.doi.org/10.1007/978-3-319-25040-3_11},
  doi = {http://doi.org/10.1007/978-3-319-25040-3_11}
}
Lenz, R. Generalized Pareto Distributions: Application to Autofocus in Automated Microscopy 2015 Selected Topics in Signal Processing, IEEE Journal of
Vol. PP(99), pp. 92-98 
article DOI  
Abstract: Dihedral filters correspond to the Fourier transform of functions defined on square grids. For gray value images there are six pairs of dihedral edge-detector pairs on 5x5 windows. In low-level image statistics the Weibull- or the generalized extreme value distributions are often used as statistical distributions modeling such filter results. Since only points with high filter magnitudes are of interest we argue that the generalized Pareto distribution is a better choice. Practically this also leads to more efficient algorithms since only a fraction of the raw filter results have to analyzed. The generalized Pareto distributions with a fixed threshold form a Riemann manifold with the Fisher information matrix as a metric tensor. For the generalized Pareto distributions we compute the determinant of the inverse Fisher information matrix as a function of the shape and scale parameters and show that it is the product of a polynomial in the shape parameter and the squared scale parameter. We then show that this determinant defines a sharpness function that can be used in autofocus algorithms. We evaluate the properties of this sharpness function with the help of a benchmark database of microscopy images with known ground truth focus positions. We show that the method based on this sharpness function results in a focus estimation that is within the given ground truth interval for a vast majority of focal sequences. Cases where it fails are mainly sequences with very poor image quality and sequences with sharp structures in different layers. The analytical structure given by the Riemann geometry of the space of probability density functions can be used to construct more efficient autofocus methods than other methods based on empirical moments.
BibTeX:
@article{Lenz2015a,
  author = {Lenz, R.},
  title = {Generalized Pareto Distributions: Application to Autofocus in Automated Microscopy},
  journal = {Selected Topics in Signal Processing, IEEE Journal of},
  year = {2015},
  volume = {PP},
  number = {99},
  pages = {92--98},
  doi = {http://doi.org/10.1109/JSTSP.2015.2482949}
}
Mochizuki, R., Kojima, T., Lenz, R. and Chao, J. Color weak compensation using local affine isometry based on discrimination threshold matching 2015 J. Optical Society of America A
Vol. 32(11), pp. 2093-2103 
article DOI  
Abstract: We develop algorithms for color-weak compensation and color-weak simulation based on Riemannian geometry
models of color spaces. The objective function introduced measures the match of color discrimination thresholds
of average normal observers and a color-weak observer. The developed matching process makes use of local affine
maps between color spaces of color-normal and color-weak observers. The method can be used to generate displays
of images that provide color-normal and color-weak observers with a similar color difference experience. It
can also be used to simulate the perception of a color-weak observer for color-normal observers. We also introduce
a new database of measurements of color discrimination threshold data for color-normal and color-weak observers
obtained at different lightness levels in CIELUV space. The compensation methods include compensations of
chromaticity using local affine maps between chromaticity planes of color-normal and color-weak observers,
and one-dimensional (1D) compensation on lightness. We describe how to determine correspondences between
the origins of local coordinates in color spaces of color-normal and color-weak observers using a neighborhood
expansion method. After matching the origins of the two coordinate systems, a local affine map is estimated by
solving a nonlinear equation, or singular-value-decomposition (SVD). We apply the methods to natural images
and evaluate their performance using the semantic differential (SD) method.
BibTeX:
@article{Mochizuki2015,
  author = {Rika Mochizuki and Takanori Kojima and Reiner Lenz and Jinhui Chao},
  title = {Color weak compensation using local affine isometry based on discrimination threshold matching},
  journal = {J. Optical Society of America A},
  year = {2015},
  volume = {32},
  number = {11},
  pages = {2093--2103},
  doi = {http://doi.org/10.1364/JOSAA.32.002093}
}
Zografos, V., Lenz, R., Ringaby, E., Felsberg, M. and Nordberg, K. Fast segmentation of sparse 3D point trajectories using group theoretical invariants 2015
Vol. 9006COMPUTER VISION - ACCV 2014, PT IV :, pp. 675-691 
inproceedings  
BibTeX:
@inproceedings{Zografos2015,
  author = {Zografos, Vasileios and Lenz, Reiner and Ringaby, Erik and Felsberg, Michael and Nordberg, Klas},
  title = {Fast segmentation of sparse 3D point trajectories using group theoretical invariants},
  booktitle = {COMPUTER VISION - ACCV 2014, PT IV :},
  year = {2015},
  volume = {9006},
  pages = {675--691}
}
Kojima, T., Mochizuki, R., Lenz, R. and Chao, J. Riemann Geometric Color-Weak Compensation for Individual Observers 2014 Universal Access in Human-Computer Interaction. Universal Access to Information and Knowledge, pp. 121-131  incollection  
BibTeX:
@incollection{Kojima2014,
  author = {Kojima, Takanori and Mochizuki, Rika and Lenz, Reiner and Chao, Jinhui},
  title = {Riemann Geometric Color-Weak Compensation for Individual Observers},
  booktitle = {Universal Access in Human-Computer Interaction. Universal Access to Information and Knowledge},
  publisher = {Springer},
  year = {2014},
  pages = {121--131}
}
Läthén, G., Lindholm, S., Lenz, R. and Borga, M. Evaluation of Transfer Function Methods in Direct Volume Rendering of the Blood Vessel Lumen 2014 Eurographics Workshop on Visual Computing for Biology and Medicine  inproceedings DOI  
BibTeX:
@inproceedings{Laethen2014,
  author = {Läthén, Gunnar and Lindholm, Stefan and Lenz, Reiner and Borga, Magnus},
  title = {Evaluation of Transfer Function Methods in Direct Volume Rendering of the Blood Vessel Lumen},
  booktitle = {Eurographics Workshop on Visual Computing for Biology and Medicine},
  publisher = {The Eurographics Association},
  year = {2014},
  doi = {http://doi.org/10.2312/vcbm.20141197}
}
Lenz, R. Generalized Extreme Value Distributions, Information Geometry and Sharpness Functions for Microscopy Images 2014 Proc. ICASSP 2014, pp. 2867-2871  inproceedings  
Abstract: We introduce the generalized extreme value distributions as
descriptors of edge-related visual appearance properties. Theoretically
these distributions are characterized by their limiting
and stability properties which gives them a role similar
to that of the normal distributions. Empirically we will show
that these distributions provide a good fit for images from a
large database of microscopy images with two visually very
different types of images. The generalized extreme value distributions
are transformed exponential distributions for which
analytical expressions for the Fisher matrix are available. We
will show how the determinant of the Fisher matrix and the
gradient of the determinant of the Fisher matrix can be used
as sharpness functions and a combination of the determinant
and the gradient information can be used to improve the quality
of the focus estimation.
BibTeX:
@inproceedings{Lenz2014,
  author = {Reiner Lenz},
  title = {Generalized Extreme Value Distributions, Information Geometry and Sharpness Functions for Microscopy Images},
  booktitle = {Proc. ICASSP 2014},
  publisher = {IEEE},
  year = {2014},
  pages = {2867--2871}
}
Andersson, T., Läthén, G., Lenz, R. and Borga, M. Modified Gradient Search for Level Set Based Image Segmentation 2013 Image Processing, IEEE Transactions on
Vol. 22(2)Image Processing, IEEE Transactions on, pp. 621-630 
article  
Abstract: Level set methods are a popular way to solve the image segmentation problem. The solution contour is found by solving an optimization problem where a cost functional is minimized. Gradient descent methods are often used to solve this optimization problem since they are very easy to implement and applicable to general nonconvex functionals. They are, however, sensitive to local minima and often display slow convergence. Traditionally, cost functionals have been modified to avoid these problems. In this paper, we instead propose using two modified gradient descent methods, one using a momentum term and one based on resilient propagation. These methods are commonly used in the machine learning community. In a series of 2-D/3-D-experiments using real and synthetic data with ground truth, the modifications are shown to reduce the sensitivity for local optima and to increase the convergence rate. The parameter sensitivity is also investigated. The proposed methods are very simple modifications of the basic method, and are directly compatible with any type of level set implementation. Downloadable reference code with examples is available online.
BibTeX:
@article{Andersson2013,
  author = {Andersson, T. and Läthén, G. and Lenz, R. and Borga, M.},
  title = {Modified Gradient Search for Level Set Based Image Segmentation},
  booktitle = {Image Processing, IEEE Transactions on},
  journal = {Image Processing, IEEE Transactions on},
  year = {2013},
  volume = {22},
  number = {2},
  pages = {621--630}
}
Lenz, R. and Zografos, V. Fisher Information and the Combination of RGB Channels 2013
Vol. LNCS-7786 Computational Color Imaging, pp. 250-264 
inproceedings  
Abstract: We introduce a method to combine the color channels of an image to a scalar valued image. Linear combinations of the RGB channels are constructed using the Fisher-Trace-Information (FTI), defined as the trace of the Fisher information matrix of the Weibull distribution, as a cost function. The FTI characterizes the local geometry of the Weibull manifold independent of the parametrization of the distribution. We show that minimizing the FTI leads to contrast enhanced images, suitable for segmentation processes. The Riemann structure of the manifold of Weibull distributions is used to design optimization methods for finding optimal weight RGB vectors. Using a threshold procedure we find good solutions even for images with limited content variation. Experiments show how the method adapts to images with widely varying visual content. Using these image dependent de-colorizations one can obtain substantially improved segmentation results compared to a mapping with pre-defined coefficients.
BibTeX:
@inproceedings{Lenz2013,
  author = {Lenz, Reiner and Zografos, Vasileios},
  title = {Fisher Information and the Combination of RGB Channels},
  booktitle = {Computational Color Imaging},
  publisher = {Springer Berlin Heidelberg},
  year = {2013},
  volume = {LNCS-7786 },
  pages = {250--264}
}
Lenz, R., Zografos, V. and Solli, M. Dihedral Color Filtering 2013 Advanced Color Image Processing and Analysis  incollection  
BibTeX:
@incollection{Lenz2012,
  author = {Reiner Lenz and Vasileios Zografos and Martin Solli},
  title = {Dihedral Color Filtering},
  booktitle = {Advanced Color Image Processing and Analysis},
  publisher = {Springer},
  year = {2013}
}
Zografos, V., Lenz, R. and Felsberg, M. The Weibull manifold in low-level image processing: an application to automatic image focusing 2013 Image and Vision Computing
Vol. 31(5), pp. 401-417 
article URL 
Abstract: Abstract In this paper, we introduce a novel framework for low-level image processing and analysis. First, we process images with very simple, difference-based filter functions. Second, we fit the 2-parameter Weibull distribution to the filtered output. This maps each image to the 2D Weibull manifold. Third, we exploit the information geometry of this manifold and solve low-level image processing tasks as minimisation problems on point sets. For a proof-of-concept example, we examine the image autofocusing task. We propose appropriate cost functions together with a simple implicitly-constrained manifold optimisation algorithm and show that our framework compares very favourably against common autofocus methods from literature. In particular, our approach exhibits the best overall performance in terms of combined speed and accuracy.
BibTeX:
@article{Zografos2013,
  author = {Zografos, Vasileios and Lenz, Reiner and Felsberg, Michael},
  title = {The Weibull manifold in low-level image processing: an application to automatic image focusing},
  journal = {Image and Vision Computing},
  year = {2013},
  volume = {31},
  number = {5},
  pages = {401--417},
  url = {http://www.sciencedirect.com/science/article/pii/S0262885613000590}
}
Läthén, G., Lenz, R., Person, A. and Borga, M. Local Adaptation of Transfer Functions for Blood Vessel Visualization 2012 Proc. SSBA 2012  inproceedings  
BibTeX:
@inproceedings{Lathen2012,
  author = {Läthén, G and Lenz, R and Person, A and Borga, M},
  title = {Local Adaptation of Transfer Functions for Blood Vessel Visualization},
  booktitle = {Proc. SSBA 2012},
  year = {2012}
}
Läthén, G., Lindholm, S., Lenz, R., Persson, A. and Borga, M. Automatic Tuning of Spatially Varying Transfer Functions for Blood Vessel Visualization 2012 Visualization and Computer Graphics, IEEE Transactions on
Vol. 18(12), pp. 2345-2354 
article DOI  
Abstract: Computed Tomography Angiography (CTA) is commonly used in clinical routine for diagnosing vascular diseases. The procedure involves the injection of a contrast agent into the blood stream to increase the contrast between the blood vessels and the surrounding tissue in the image data. CTA is often visualized with Direct Volume Rendering (DVR) where the enhanced image contrast is important for the construction of Transfer Functions (TFs). For increased efficiency, clinical routine heavily relies on preset TFs to simplify the creation of such visualizations for a physician. In practice, however, TF presets often do not yield optimal images due to variations in mixture concentration of contrast agent in the blood stream. In this paper we propose an automatic, optimization-based method that shifts TF presets to account for general deviations and local variations of the intensity of contrast enhanced blood vessels. Some of the advantages of this method are the following. It computationally automates large parts of a process that is currently performed manually. It performs the TF shift locally and can thus optimize larger portions of the image than is possible with manual interaction. The method is based on a well known vesselness descriptor in the definition of the optimization criterion. The performance of the method is illustrated by clinically relevant CT angiography datasets displaying both improved structural overviews of vessel trees and improved adaption to local variations of contrast concentration.
BibTeX:
@article{Lathen2012a,
  author = {Läthén, G. and Lindholm, S. and Lenz, R. and Persson, A. and Borga, M.},
  title = {Automatic Tuning of Spatially Varying Transfer Functions for Blood Vessel Visualization},
  journal = {Visualization and Computer Graphics, IEEE Transactions on},
  year = {2012},
  volume = {18},
  number = {12},
  pages = {2345--2354},
  doi = {http://doi.org/10.1109/TVCG.2012.203}
}
Lenz, R. and Zografos, V. From Color to Gray via the Weibull Manifold 2012 Proc. SSBA 2012  inproceedings  
BibTeX:
@inproceedings{Lenz2012a,
  author = {Lenz, R and Zografos, V.},
  title = {From Color to Gray via the Weibull Manifold},
  booktitle = {Proc. SSBA 2012},
  year = {2012}
}
Lenz, R. and Zografos, V. RGB Filter design using the properties of theWeibull Manifold 2012 Proc. 6th European Conference on Colour in Graphics, Imaging, and Vision, pp. 200-205  inproceedings  
Abstract: Combining the channels of a multi-band image with the help of a pixelwise weighted sum is one of the basic operations in color and multispectral image processing. A typical example is the conversion of RGB- to intensity images. Usually the weights are given by some standard values or chosen heuristically. This does not take into account neither the statistical nature of the image source nor the intended further processing of the scalar image. In this paper we will present a framework in which we specify the statistical properties of the input data with the help of a representative collection of image patches. On the output side we specify the intended processing of the scalar image with the help of a filter kernel with zero-mean filter coefficients. Given the image patches and the filter kernel we use the Fisher information of the manifold of two-parameter Weibull distributions to introduce the trace of the Fisher information matrix as a cost function on the space of weight vectors of unit length. We will illustrate the properties of the method with the help of a database of scanned leaves and some color images from the internet. For the green leaves we find that the result of the mapping is similar to standard mappings like Matlabï¿?s RGB2Gray weights. We then change the colour of the leaf using a global shift in the HSV representation of the original image and show how the proposed mapping adapts to this color change. This is also confirmed with other natural images where the new mapping reveals much more subtle details in the processed image. In the last experiment we show that the mapping emphasizes visually salient points in the image whereas the standard mapping only emphasizes global intensity changes. The proposed approach to RGB filter design provides thus a new methodology based only on the properties of the image statistics and the intended post-processing. It adapts to color changes of the input images and, due to its foundation in the statistics of extreme-value distributions, it is suitable for detecting salient regions in an image.
BibTeX:
@inproceedings{Lenz2012b,
  author = {Reiner Lenz and Vasileios Zografos},
  title = {RGB Filter design using the properties of theWeibull Manifold},
  booktitle = {Proc. 6th European Conference on Colour in Graphics, Imaging, and Vision},
  publisher = {Society for Imaging Science and Technology, Springfield, VA 22151 USA},
  year = {2012},
  pages = {200--205}
}
Oshima, S., Mochizuki, R., Lenz, R. and Chao, J. Color-Weakness Compensation using Riemann Normal Coordinates 2012 Proceedings IEEE International Symposium on Multimedia (ISM2012), pp. 175-178  inproceedings DOI  
Abstract: We introduce normal coordinates in Riemann spaces as a tool to construct color-weak compensation methods. We use them to compute color stimuli for a color weak observers that result in the same color perception as the original image presented to a color normal observer in the sense that perceived color-differences are identical for both. The compensation is obtained through a color-difference-preserving map, i.e. an isometry between the 3D color spaces of a colornormal and any given color-weak observer. This approach uses discrimination threshold data and is free from approximation errors due to local linearization. The performance is evaluated with the help of semantic differential (SD) tests.
BibTeX:
@inproceedings{Oshima2012,
  author = {Satoshi Oshima and Rika Mochizuki and Reiner Lenz and Jinhui Chao},
  title = {Color-Weakness Compensation using Riemann Normal Coordinates},
  booktitle = {Proceedings IEEE International Symposium on Multimedia (ISM2012)},
  publisher = {IEEE Comp},
  year = {2012},
  pages = {175--178},
  doi = {http://doi.org/10.1109/ISM.2012.42}
}
Åström, F., Felsberg, M. and Lenz, R. Color Persistent Anisotropic Diffusion of Images 2011
Vol. 6688 Image Analysis, pp. 262-272 
inproceedings  
Abstract: Techniques from the theory of partial differential equations are often used to design filter methods that are locally adapted to the image structure. These techniques are usually used in the investigation of gray-value images. The extension to color images is non-trivial, where the choice of an appropriate color space is crucial. The RGB color space is often used although it is known that the space of human color perception is best described in terms of non-euclidean geometry, which is fundamentally different from the structure of the RGB space. Instead of the standard RGB space, we use a simple color transformation based on the theory of finite groups. It is shown that this transformation reduces the color artifacts originating from the diffusion processes on RGB images. The developed algorithm is evaluated on a set of real-world images, and it is shown that our approach exhibits fewer color artifacts compared to state-of-the-art techniques. Also, our approach preserves details in the image for a larger number of iterations.
BibTeX:
@inproceedings{LNCS66880262,
  author = {Freddie Åström and Michael Felsberg and Reiner Lenz},
  title = {Color Persistent Anisotropic Diffusion of Images},
  booktitle = { Image Analysis},
  publisher = {Springer},
  year = {2011},
  volume = {6688},
  pages = {262--272}
}
Åström, F., Felsberg, M. and Lenz, R. Structure Preserving Anisotropic Diffusion of Vector Valued Images 2011 Proc. SSBA Symposium  inproceedings  
BibTeX:
@inproceedings{AAstrom2011,
  author = {Åström, F. and Felsberg, M. and Lenz, R.},
  title = {Structure Preserving Anisotropic Diffusion of Vector Valued Images},
  booktitle = {Proc. SSBA Symposium},
  year = {2011}
}
Mochizuki, R., Oshima, S., Lenz, R. and Chao, J. Exact Compensation of Color-Weakness with Discrimination Threshold Matching 2011 Universal Access in HCI, Part IV, HCII 2011, pp. 155-164  inproceedings  
BibTeX:
@inproceedings{Mochizuki2011a,
  author = {Rika Mochizuki and Satoshi Oshima and Reiner Lenz and Jinhui Chao},
  title = {Exact Compensation of Color-Weakness with Discrimination Threshold Matching},
  booktitle = {Universal Access in HCI, Part IV, HCII 2011},
  publisher = {Springer},
  year = {2011},
  pages = {155--164}
}
Solli, M. Color Emotions in Large Scale Content Based Image Indexing 2011 School: Linköping University  phdthesis URL 
Abstract: Traditional content based image indexing aims at developing algorithms that can analyze and index images based on their visual content. A typical approach is to measure image attributes, like colors or textures, and save the result in image descriptors, which then can be used in recognition and retrieval applications. Two topics within content based image indexing are addressed in this thesis: Emotion based image indexing, and font recognition. The main contribution is the inclusion of high-level semantics in indexing of multi-colored images. We focus on color emotions and color harmony, and introduce novel emotion and harmony based image descriptors, including global emotion histograms, a bag-of-emotions descriptor, an image harmony descriptor, and an indexing method based on Kobayashi's Color Image Scale. The first three are based on models from color science, analyzing emotional properties of single colors or color combinations. A majority of the descriptors are evaluated in psychophysical experiments. The results indicate that observers perceive color emotions and color harmony for multi-colored images in similar ways, and that observer judgments correlate with values obtained from the presented descriptors. The usefulness of the descriptors is illustrated in large scale image classification experiments involving emotion related image categories, where the presented descriptors are compared with global and local standard descriptors within this field of research. We also investigate if these descriptors can predict the popularity of images. Three image databases are used in the experiments, one obtained from an image provider, and two from a major image search service. The two from the search service were harvested from the Internet, containing image thumbnails together with keywords and user statistics. One of them is a traditional object database, whereas the other is a unique database focused on emotional image categories. A large part of the emotion database has been released to the research community. The second contribution is visual font recognition. We implemented a font search engine, capable of handling very large font databases. The input to the search engine is an image of a text line, and the output is the name of the font used when rendering the text. After pre-processing and segmentation of the input image, eigenimages are used, where features are calculated for individual characters. The performance of the search engine is illustrated with a database containing more than 2700 fonts. A system for visualizing the entire font database is also presented. Both the font search engine, and the descriptors that are related to emotions and harmony are implemented in publicly available search engines. The implementations are presented together with user statistics.
BibTeX:
@phdthesis{Solli2011a,
  author = {Martin Solli},
  title = {Color Emotions in Large Scale Content Based Image Indexing},
  school = {Linköping University},
  year = {2011},
  url = {http://liu.diva-portal.org/smash/get/diva2:392872/FULLTEXT01}
}
Solli, M. and Lenz, R. A Font Search Engine for Large Font Databases 2011 ELCVIA Electronic Letters on Computer Vision and Image Analysis
Vol. 10(1), pp. 24-41 
article  
BibTeX:
@article{Solli2011,
  author = {Solli, Martin and Lenz, Reiner},
  title = {A Font Search Engine for Large Font Databases},
  journal = {ELCVIA Electronic Letters on Computer Vision and Image Analysis},
  year = {2011},
  volume = {10},
  number = {1},
  pages = {24--41}
}
Solli, M. and Lenz, R. Color emotions for multi-colored images 2011 Color Res. Appl.
Vol. 36(3), pp. 210-221 
article URL 
Abstract: Abstract We investigate the emotional response to colors in ordinary multicolored images. In psychophysical experiments, using both category scaling and interval scaling, observers are asked to judge images using three emotion factors: activity, weight, and heat. The color emotion metric was originally developed for single colors, and later extended to include pairs of colors. The same metric was recently used in image retrieval. The results show that people in general perceive color emotions for multi-colored images in similar ways, and that observer judgments correlate with the recently proposed method used in image retrieval. The intended usage is in retrieval systems publicly available on the Internet, where both the user and the viewing environment is unknown, which requires novel ways of conducting the psychophysical experiments. © 2010 Wiley Periodicals, Inc. Col Res Appl, 36, 210–221, 2011;
BibTeX:
@article{Solli2011b,
  author = {Solli, Martin and Lenz, Reiner},
  title = {Color emotions for multi-colored images},
  journal = {Color Res. Appl.},
  publisher = {Wiley},
  year = {2011},
  volume = {36},
  number = {3},
  pages = {210--221},
  url = {http://dx.doi.org/10.1002/col.20604}
}
Solli, M. and Lenz, R. Content Based Detection of Popular Images in Large Image Databases 2011
Vol. LNCS-6688 Image Analysis, pp. 218-227 
inproceedings  
Abstract: We investigate the use of standard image descriptors and a supervised learning algorithm for estimating the popularity of images. The intended application is in large scale image search engines, where the proposed approach can enhance the user experience by improving the sorting of images in a retrieval result. Classification methods are trained and evaluated on real-world user statistics recorded by a major image search engine. The conclusion is that for many image categories, the combination of supervised learning algorithms and standard image descriptors results in useful popularity predictions.
BibTeX:
@inproceedings{LNCS66880218,
  author = {Martin Solli and Reiner Lenz},
  title = {Content Based Detection of Popular Images in Large Image Databases},
  booktitle = { Image Analysis},
  publisher = {Springer},
  year = {2011},
  volume = {LNCS-6688},
  pages = {218--227}
}
Zografos, V. and Lenz, R. Fast Algebraic Transforms and Extreme Value Theory 2011 Proc. SSBA  inproceedings  
BibTeX:
@inproceedings{Zografos2011a,
  author = {Zografos, V. and Lenz, R},
  title = {Fast Algebraic Transforms and Extreme Value Theory},
  booktitle = {Proc. SSBA},
  year = {2011}
}
Zografos, V. and Lenz, R. Spatio-chromatic Image Content Descriptors and Their Analysis Using Extreme Value Theory 2011
Vol. 6688Image Analysis, pp. 579-591 
inproceedings  
Abstract: We use the theory of group representations to construct very fast image descriptors that split the vector space of local RGB distributions into small group-invariant subspaces. These descriptors are group theoretical generalizations of the Fourier Transform and can be computed with algorithms similar to the FFT. Because of their computational efficiency they are especially suitable for retrieval, recognition and classification in very large image datasets. We also show that the statistical properties of these descriptors are governed by the principles of the Extreme Value Theory (EVT). This enables us to work directly with parametric probability distribution models, which offer a much lower dimensionality and higher resolution and flexibility than histogram representations. We explore the connection to EVT and analyse the characteristics of these descriptors from a probabilistic viewpoint with the help of large image databases.
BibTeX:
@inproceedings{Zografos2011,
  author = {Vasileios Zografos and Reiner Lenz},
  title = {Spatio-chromatic Image Content Descriptors and Their Analysis Using Extreme Value Theory},
  booktitle = {Image Analysis},
  publisher = {Springer},
  year = {2011},
  volume = {6688},
  pages = {579--591}
}
Kohei, T., Chao, J. and Lenz, R. On Curvature of Color Spaces and its Implications 2010 Proceedings 5th European Conference on Colour in Graphics, Imaging, and Vision, pp. 393-398  inproceedings URL 
BibTeX:
@inproceedings{Kohei2010,
  author = {Toko Kohei and Jinhui Chao and Reiner Lenz},
  title = {On Curvature of Color Spaces and its Implications},
  booktitle = {Proceedings 5th European Conference on Colour in Graphics, Imaging, and Vision},
  year = {2010},
  pages = {393--398},
  url = {http://webstaff.itn.liu.se/ reile/prints/CGIV10_KOHEI_PG393.pdf}
}
Lenz, R. and Latorre Carmona, P. Hierarchical S(3)-coding of RGB histograms 2010 Commun. Comput. Info. Sci.
Vol. 68 CCISInternational Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, VISIGRAPP 2009, pp. 188-200 
incollection  
BibTeX:
@incollection{Lenz2010d,
  author = {Lenz, R. and Latorre Carmona, P.},
  title = {Hierarchical S(3)-coding of RGB histograms},
  booktitle = {International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, VISIGRAPP 2009},
  journal = {Commun. Comput. Info. Sci.},
  publisher = {Springer Verlag},
  year = {2010},
  volume = {68 CCIS},
  pages = {188--200}
}
Lenz, R., Mochizuki, R. and Chao, J. Iwasawa Decomposition and Computational Riemannian Geometry 2010 Proc. ICPR, pp. 4472-4475  inproceedings  
BibTeX:
@inproceedings{Lenz2010b,
  author = {Reiner Lenz and Rika Mochizuki and Jinhui Chao},
  title = {Iwasawa Decomposition and Computational Riemannian Geometry},
  booktitle = {Proc. ICPR},
  publisher = {IEEE},
  year = {2010},
  pages = {4472--4475}
}
Lenz, R., Mochizuki, R. and Chao, J. We KAN 2010 (34)Proceedings SSBA 2010, pp. 19-22  inproceedings  
Abstract: We investigate several topics related to manifold-techniques for signal processing. On the most general level we consider manifolds with a Riemannian Geometry. These manifolds are characterized by their inner products on the tangent spaces. We describe the connection between the symmetric positive-definite matrices defining these inner products and the Cartan and the Iwasawa decomposition of the general linear matrix groups. This decomposition gives rise to the decomposition of the inner product matrices into diagonal matrices and orthonormal and into diagonal and upper triangular matrices. Next we describe the estimation of the inner product matrices from measured data as an optimization process on the homogeneous space of upper triangular matrices. We show that the decomposition leads to simple forms of gradients and Hessian matrices that are commonly used in optimization algorithms. Using the parametrization from the symmetric space ensures also that all intermediate estimates of the inner product matrix are symmetric and positive definite. Finally we apply the method to a problem from psychophysics where the color perception properties of an observer are characterized with the help of color matching experiments. We will show that measurements from color weak observers require the enforcement of the positive-definiteness of the matrix with the help of the manifold optimization technique.
BibTeX:
@inproceedings{Lenz2010a,
  author = {Reiner Lenz and Rika Mochizuki and Jinhui Chao},
  title = {We KAN},
  booktitle = {Proceedings SSBA 2010},
  year = {2010},
  number = {34},
  pages = {19--22}
}
Lenz, R. and Solli, M. Dihedral Groups and Spatio-Chromatic Filter Systems 2010 16. Workshop Farbbildverarbeitung, pp. 51-62  inproceedings URL 
Abstract: The dihedral groups D(4) and D(3) are the symmetry groups of the image grid and the RGB color channels respectively. The product group dtg is therefore a symmetry group of RGB patches. Using the representation theory of the product group we construct very fast digital filter systems that split the vector space of RGB distributions into minimal group-invariant subspaces. We show that these filter systems can be implemented using additions/subtractions only and that the number of arithmetic operations can be minimized using algebraically defined fast algorithms. The raw filter results are then converted into a polar coordinate system in which the radial component is invariant under all group operations of the original distributions. The angular part encodes the effect of the group operation. We illustrate the performance of these filters by investigating the internal structure of two databases containing approximately 1.5 million images crawled by the Picsearch image search engine. One of the databases contains images indexed with object-related keywords while the second database is organized in emotion-related categories. We characterize images by the statistical distributions of the filter results from the different blocks and use parameters derived from these distributions to characterize the different categories. We also use a standard support vector machine to illustrate the separability of images from different category pairs. The examples illustrate that, despite their simplicity, the features extract relevant visual properties that can be used for indexing, retrieval and classification.
BibTeX:
@inproceedings{Lenz2010c,
  author = {Reiner Lenz and Martin Solli},
  title = {Dihedral Groups and Spatio-Chromatic Filter Systems},
  booktitle = {16. Workshop Farbbildverarbeitung},
  publisher = {Zentrum fï¿?r Bild und Signalverarbeitung e.V. ISBN 978-3-00-032504-5},
  year = {2010},
  pages = {51--62},
  url = {http://webstaff.itn.liu.se/ reile/prints/fws-ilmenau-2010.pdf}
}
Solli, M. and Lenz, R. Color Semantics for Image Indexing 2010 Proceedings 5th European Conference on Colour in Graphics, Imaging, and Vision, pp. 353-358  inproceedings URL 
Abstract: We propose a color-based image descriptor that can be used for image indexing based on high-level semantic concepts. The descriptor is based on Kobayashi's Color Image Scale, which is a system that includes 130 basic colors combined in 1170 three-color combinations. Each combination is labeled with one of 180 high-level semantic concepts, like "elegant", "romantic", "provocative", etc. Moreover, words are located in a two-dimensional semantic space, and arranged into groups based on perceived similarity. From a modified approach for statistical analysis of images, involving transformations of ordinary RGB-histograms, a semantic image descriptor is derived, containing semantic information about both color combinations and single colors in the image. We show how the descriptor can be translated into different levels of semantic information, and used in indexing of multi-colored images. Intended applications are, for instance, image labeling and retrieval.
BibTeX:
@inproceedings{Solli2010,
  author = {Martin Solli and Reiner Lenz},
  title = {Color Semantics for Image Indexing},
  booktitle = {Proceedings 5th European Conference on Colour in Graphics, Imaging, and Vision},
  publisher = {IS&T},
  year = {2010},
  pages = {353--358},
  url = {http://webstaff.itn.liu.se/ reile/prints/CGIV10_SOLLI_PG353.pdf}
}
Solli, M. and Lenz, R. Emotion related structures in large image databases 2010 Proceedings of the ACM International Conference on Image and Video Retrieval, pp. 398-405  inproceedings DOI  
BibTeX:
@inproceedings{Solli2010c,
  author = {Solli, Martin and Lenz, Reiner},
  title = {Emotion related structures in large image databases},
  booktitle = {Proceedings of the ACM International Conference on Image and Video Retrieval},
  publisher = {ACM},
  year = {2010},
  pages = {398--405},
  doi = {http://doi.org/10.1145/1816041.1816099}
}
Andersson, T., Läthén, G., Lenz, R. and Borga, M. A Fast Optimization Method for Level Set Segmentation 2009 Image AnalysisProceedings 16th Scandinavian Conference, SCIA 2009, pp. 400-409  inproceedings URL 
Abstract: Level set methods are a popular way to solve the image segmentation problem in computer image analysis. A contour is implicitly represented by the zero level of a signed distance function, and evolved according to a motion equation in order to minimize a cost function. This function defines the objective of the segmentation problem and also includes regularization constraints. Gradient descent search is the de facto method used to solve this optimization problem. Basic gradient descent methods, however, are sensitive for local optima and often display slow convergence. Traditionally, the cost functions have been modified to avoid these problems. In this work, we instead propose using a modified gradient descent search based on resilient propagation (Rprop), a method commonly used in the machine learning community. Our results show faster convergence and less sensitivity to local optima, compared to traditional gradient descent.
BibTeX:
@inproceedings{Andersson2009,
  author = {Thord Andersson and Gunnar Läthén and Reiner Lenz and Magnus Borga},
  title = {A Fast Optimization Method for Level Set Segmentation},
  booktitle = {Proceedings 16th Scandinavian Conference, SCIA 2009},
  journal = {Image Analysis},
  publisher = {Springer},
  year = {2009},
  pages = {400--409},
  note = {Oslo, Norway, June 15-18, 2009.},
  url = {http://dx.doi.org/10.1007/978-3-642-02230-2_41}
}
Läthén, G., Andersson, T., Lenz, R. and Borga, M. Level set based segmentation using gradient descent with momentum 2009 SSBA 2009, Symposium on image analysis,2009, pp. 1-4  inproceedings DOI URL 
BibTeX:
@inproceedings{Lath'en2009a,
  author = {Läthén, Gunnar and Andersson, Thord and Lenz, Reiner and Borga, Magnus},
  title = {Level set based segmentation using gradient descent with momentum},
  booktitle = {SSBA 2009, Symposium on image analysis,2009},
  publisher = {Halmstad University},
  year = {2009},
  pages = {1--4},
  url = {http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-45370},
  doi = {urn:nbn:se:liu:diva-45370}
}
Läthén, G., Andersson, T., Lenz, R. and Borga, M. Momentum Based Optimization Methods for Level Set Segmentation 2009 Scale Space and Variational Methods in Computer VisionProceedings Second International Conference, SSVM 2009, Voss, pp. 124-136  inproceedings URL 
Abstract: Segmentation of images is often posed as a variational problem. As such, it is solved by formulating an energy functional depending on a contour and other image derived terms. The solution of the segmentation problem is the contour which extremizes this functional. The standard way of solving this optimization problem is by gradient descent search in the solution space, which typically suffers from many unwanted local optima and poor convergence. Classically, these problems have been circumvented by modifying the energy functional. In contrast, the focus of this paper is on alternative methods for optimization. Inspired by ideas from the machine learning community, we propose segmentation based on gradient descent with momentum. Our results show that typical models hampered by local optima solutions can be further improved by this approach. We illustrate the performance improvements using the level set framework.
BibTeX:
@inproceedings{Lath'en2009,
  author = {Gunnar Läthén and Thord Andersson and Reiner Lenz and Magnus Borga},
  title = {Momentum Based Optimization Methods for Level Set Segmentation},
  booktitle = {Proceedings Second International Conference, SSVM 2009, Voss},
  journal = {Scale Space and Variational Methods in Computer Vision},
  publisher = {Springer},
  year = {2009},
  pages = {124--136},
  url = {http://dx.doi.org/10.1007/978-3-642-02256-2_11}
}
Lenz, R. Octahedral Filters for 3D Image Processing 2009 Proceedings SSBA 2009, pp. 109-112  inproceedings  
BibTeX:
@inproceedings{Lenz2009,
  author = {Reiner Lenz},
  title = {Octahedral Filters for 3D Image Processing},
  booktitle = {Proceedings SSBA 2009},
  year = {2009},
  pages = {109--112}
}
Lenz, R. and Carmona, P.L. Transform Coding of RGB-Histograms 2009 International Conference on Computer Vision Theory and Applications (VISAPP), pp. 117-124  inproceedings URL 
BibTeX:
@inproceedings{Lenz2009a,
  author = {Reiner Lenz and Pedro Latorre Carmona},
  title = {Transform Coding of RGB-Histograms},
  booktitle = {International Conference on Computer Vision Theory and Applications (VISAPP)},
  year = {2009},
  pages = {117--124},
  note = {ISBN: 978-989-8111-69-2},
  url = {http://webstaff.itn.liu.se/ reile/prints/VisApp2009.pdf}
}
Lenz, R. and Latorre Carmona, P. Octahedral Transforms for 3-D Image Processing 2009 Image Processing, IEEE Transactions on
Vol. 18(12)Image Processing, IEEE Transactions on, pp. 2618-2628 
article URL 
Abstract: The octahedral group is one of the finite subgroups of the rotation group in 3-D Euclidean space and a symmetry group of the cubic grid. Compression and filtering of 3-D volumes are given as application examples of its representation theory. We give an overview over the finite subgroups of the 3-D rotation group and their classification. We summarize properties of the octahedral group and basic results from its representation theory. Wide-sense stationary processes are processes with group theoretical symmetries whose principal components are closely related to the representation theory of their symmetry group. Linear filter systems are defined as projection operators and symmetry-based filter systems are generalizations of the Fourier transforms. The algorithms are implemented in Maple/Matlab functions and worksheets. In the experimental part, we use two publicly available MRI volumes. It is shown that the assumption of wide-sense stationarity is realistic and the true principal components of the correlation matrix are very well approximated by the group theoretically predicted structure. We illustrate the nature of the different types of filter systems, their invariance and transformation properties. Finally, we show how thresholding in the transform domain can be used in 3-D signal processing.
BibTeX:
@article{Lenz2009b,
  author = {Lenz, R. and Latorre Carmona, P.},
  title = {Octahedral Transforms for 3-D Image Processing},
  booktitle = {Image Processing, IEEE Transactions on},
  journal = {Image Processing, IEEE Transactions on},
  year = {2009},
  volume = {18},
  number = {12},
  pages = {2618--2628},
  url = {http://webstaff.itn.liu.se/ reile/prints/ieeeip-2009.pdf}
}
Lenz, R., Oshima, S., Mochizuki, R. and Chao, J. An Invariant Metric on the Manifold of Second Order Moments 2009 IEEE Color and Reflectance in Imaging and Computer Vision Workshop 2009 - CRICV 2009, pp. 1923-1930  inproceedings DOI URL 
BibTeX:
@inproceedings{Lenz2009c,
  author = {Lenz, Reiner and Oshima, Satoshi and Mochizuki, Rika and Chao, Jinhui},
  title = {An Invariant Metric on the Manifold of Second Order Moments},
  booktitle = {IEEE Color and Reflectance in Imaging and Computer Vision Workshop 2009 - CRICV 2009},
  publisher = {IEEE-Computer Society},
  year = {2009},
  pages = {1923--1930},
  url = {http://webstaff.itn.liu.se/ reile/prints/iccv2009w_251.pdf},
  doi = {urn:nbn:se:liu:diva-25579}
}
Ohshima, S., Mochizuki, R., Chao, J. and Lenz, R. Color Reproduction Using Riemann Normal Coordinates 2009 Computational Color Imaging
Vol. 5646Second International Workshop, CCIW 2009. Revised Selected Papers, pp. 140-149 
inproceedings DOI URL 
Abstract: In this paper we use tools from Riemann geometry to construct color reproduction methods that take into account the varying color perception properties of observers. We summarize the different steps in the processing: the estimation of the discrimination thresholds, the estimation of the Riemann metric, the construction of the metric-preserving or color-difference-preserving mapping and the usage of Semantic Differentiation (SD) techniques in the evaluation. We tested the method by measuring the discrimination data for 45 observers. We illustrate the geometric properties of the color spaces obtained and show the result of the metric-preserving maps between the color space of color-normal observers and a color-weak observer. We then apply the obtained maps to produce color corrected reproductions of two natural images.
BibTeX:
@inproceedings{Ohshima2009,
  author = {Ohshima, Satoshi and Mochizuki, Rika and Chao, Jinhui and Lenz, Reiner},
  title = {Color Reproduction Using Riemann Normal Coordinates},
  booktitle = {Second International Workshop, CCIW 2009. Revised Selected Papers},
  journal = {Computational Color Imaging},
  publisher = {Springer},
  year = {2009},
  volume = {5646},
  pages = {140--149},
  url = {http://webstaff.itn.liu.se/ reile/prints/cciw2009.pdf},
  doi = {http://doi.org/10.1007/978-3-642-03265-3_15}
}
Solli, M. and Lenz, R. Color Based Bags-of-Emotions 2009 Computer Analysis of Images and Patterns
Vol. 5702Proceedings Computer Analysis of Images and Patterns (CAIP 2009), pp. 573-580 
inproceedings DOI URL 
Abstract: In this paper we describe how to include high level semantic information, such as aesthetics and emotions, into Content Based Image Retrieval. We present a color-based emotion-related image descriptor that can be used for describing the emotional content of images. The color emotion metric used is derived from psychophysical experiments and based on three variables: activity, weight and heat. It was originally designed for single-colors, but recent research has shown that the same emotion estimates can be applied in the retrieval of multi-colored images. Here we describe a new approach, based on the assumption that perceived color emotions in images are mainly affected by homogenous regions, defined by the emotion metric, and transitions between regions. RGB coordinates are converted to emotion coordinates, and for each emotion channel, statistical measurements of gradient magnitudes within a stack of low-pass filtered images are used for finding interest points corresponding to homogeneous regions and transitions between regions. Emotion characteristics are derived for patches surrounding each interest point, and saved in a bag-of-emotions, that, for instance, can be used for retrieving images based on emotional content.
BibTeX:
@inproceedings{Solli2009b,
  author = {Solli, Martin and Lenz, Reiner},
  title = {Color Based Bags-of-Emotions},
  booktitle = {Proceedings Computer Analysis of Images and Patterns (CAIP 2009)},
  journal = {Computer Analysis of Images and Patterns},
  publisher = {Springer},
  year = {2009},
  volume = {5702},
  pages = {573--580},
  url = {http://webstaff.itn.liu.se/ reile/prints/CAIP2009.pdf},
  doi = {http://doi.org/10.1007/978-3-642-03767-2}
}
Solli, M. and Lenz, R. Color Harmony for Image Indexing 2009 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops, pp. 1885-1892  inproceedings DOI URL 
BibTeX:
@inproceedings{Solli2009,
  author = {Solli, Martin and Lenz, Reiner},
  title = {Color Harmony for Image Indexing},
  booktitle = {2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops},
  year = {2009},
  pages = {1885--1892},
  url = {http://webstaff.itn.liu.se/ reile/prints/iccv2009w_246.pdf},
  doi = {urn:nbn:se:liu:diva-21923}
}
Solli, M. and Lenz, R. Visualization of large font databases 2009 Proc. IARIGAI 2009  inproceedings  
BibTeX:
@inproceedings{Solli2009a,
  author = {Martin Solli and Reiner Lenz},
  title = {Visualization of large font databases},
  booktitle = {Proc. IARIGAI 2009},
  year = {2009}
}
Chao, J., Lenz, R., Matsumoto, D. and Nakamura, T. Riemann Geometry for Color Characterization and Mapping 2008 Proc. CGIV 2008, pp. 277-282  inproceedings DOI URL 
BibTeX:
@inproceedings{Chao2008,
  author = {Chao, Jinhui and Lenz, Reiner and Matsumoto, Daisuke and Nakamura, Tatsuya},
  title = {Riemann Geometry for Color Characterization and Mapping},
  booktitle = {Proc. CGIV 2008},
  publisher = {Society for Imaging Science and Technology},
  year = {2008},
  pages = {277--282},
  url = {http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-42580},
  doi = {urn:nbn:se:liu:diva-42580}
}
Heikkinen, V., Lenz, R., Jetsu, T., Parkkinen, J., Hauta-Kasari, M. and Jaaskelainen, T. Evaluation and unification of some methods for estimating reflectance spectra from RGB images 2008 J. Opt. Soc. Am. A
Vol. 25(10), pp. 2444-2458 
article URL 
Abstract: The problem of estimating spectral reflectances from the responses of a digital camera has received considerable attention recently. This problem can be cast as a regularized regression problem or as a statistical inversion problem. We discuss some previously suggested estimation methods based on critically undersampled RGB measurements and describe some relations between them. We concentrate mainly on those models that are using a priori information in the form of high-resolution measurements. We use the ï¿?kernel machineï¿? framework in our evaluations and concentrate on the use of multiple illuminations and on the investigation of the performance of global and locally adapted estimation methods. We also introduce a nonlinear transformation of reflectance values to ensure that the estimated reflection spectra fulfill physically motivated boundary conditions. The reported experimental results are derived from measured and simulated camera responses from the Munsell Matte, NCS, and Pantone data sets.
BibTeX:
@article{Heikkinen2008a,
  author = {Heikkinen, Ville and Lenz, Reiner and Jetsu, Tuija and Parkkinen, Jussi and Hauta-Kasari, Markku and Jaaskelainen, Timo},
  title = {Evaluation and unification of some methods for estimating reflectance spectra from RGB images},
  journal = {J. Opt. Soc. Am. A},
  publisher = {OSA},
  year = {2008},
  volume = {25},
  number = {10},
  pages = {2444--2458},
  url = {http://josaa.osa.org/abstract.cfm?URI=josaa-25-10-2444}
}
Heikkinen, V., Lenz, R., Jetsu, T., Parkkinen, J. and Jaaskleainen, T. Estimation of Reflectance Spectra Using Multiple Illuminations 2008 Proc. CGIV 2008, pp. 272-276  inproceedings DOI URL 
BibTeX:
@inproceedings{Heikkinen2008,
  author = {Heikkinen, Ville and Lenz, Reiner and Jetsu, Tuija and Parkkinen, Jussi and Jaaskleainen, Timo},
  title = {Estimation of Reflectance Spectra Using Multiple Illuminations},
  booktitle = {Proc. CGIV 2008},
  publisher = {Society for Imaging Science and Technology},
  year = {2008},
  pages = {272--276},
  url = {http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-42581},
  doi = {urn:nbn:se:liu:diva-42581}
}
Lenz, R. Lie methods for color robot vision 2008 Robotica
Vol. 26(4), pp. 453-464 
article URL 
Abstract: We describe how Lie-theoretical methods can be used to analyze color related problems in machine vision. The basic observation is that the nonnegative nature of spectral color signals restricts these functions to be members of a limited, conical section of the larger Hilbert space of square-integrable functions. From this observation, we conclude that the space of color signals can be equipped with a coordinate system consisting of a half-axis and a unit ball with the Lorentz groups as natural transformation group. We introduce the theory of the Lorentz group SU(1, 1) as a natural tool for analyzing color image processing problems and derive some descriptions and algorithms that are useful in the investigation of dynamical color changes. We illustrate the usage of these results by describing how to compress, interpolate, extrapolate, and compensate image sequences generated by dynamical color changes. ? 2007 Cambridge University Press.
BibTeX:
@article{Lenz2008,
  author = {Lenz, R.},
  title = {Lie methods for color robot vision},
  journal = {Robotica},
  year = {2008},
  volume = {26},
  number = {4},
  pages = {453--464},
  url = {http://www.scopus.com/scopus/inward/record.url?eid=2-s2.0-47849116072&partnerID=40&rel=R8.0.0}
}
Lenz, R. Structures in Spaces of RGB Histograms 2008 14. Workshop Farbbildverarbeitung, Aachen, 1.-2. Oktober 2008, pp. 13-22  inproceedings DOI URL 
BibTeX:
@inproceedings{Lenz2008a,
  author = {Lenz, Reiner},
  title = {Structures in Spaces of RGB Histograms},
  booktitle = {14. Workshop Farbbildverarbeitung, Aachen, 1.-2. Oktober 2008},
  publisher = {Shaker Verlag},
  year = {2008},
  pages = {13--22},
  url = {http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-43080},
  doi = {urn:nbn:se:liu:diva-43080}
}
Mochizuki, R., Nakamura, T., Chao, J. and Lenz, R. Correction of Color-Weakness by Matching of Discrimination Thresholds 2008 Proc. CGIV 2008, pp. 208-213  inproceedings DOI URL 
BibTeX:
@inproceedings{Mochizuki2008,
  author = {Mochizuki, Rika and Nakamura, Tatsuya and Chao, Jinhui and Lenz, Reiner},
  title = {Correction of Color-Weakness by Matching of Discrimination Thresholds},
  booktitle = {Proc. CGIV 2008},
  publisher = {The Society for Imaging Science and Technology},
  year = {2008},
  pages = {208--213},
  url = {http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-42579},
  doi = {urn:nbn:se:liu:diva-42579}
}
Solli, M. and Lenz, R. Color Emotions for Image Classification and Retrieval 2008 Proc. CGIV 2008, pp. 367-371  inproceedings DOI URL 
BibTeX:
@inproceedings{Solli2008,
  author = {Solli, Martin and Lenz, Reiner},
  title = {Color Emotions for Image Classification and Retrieval},
  booktitle = {Proc. CGIV 2008},
  publisher = {Society for Imaging Science and Technology},
  year = {2008},
  pages = {367--371},
  url = {http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-42582},
  doi = {urn:nbn:se:liu:diva-42582}
}
Solli, M. and Lenz, R. Emotional Satisfaction in Color Image Retrieval 2008 Proceedings Swedish Symposium on Image Analysis 2008, pp. 7-10  inproceedings  
BibTeX:
@inproceedings{Solli2008a,
  author = {Solli, M. and Lenz, R.},
  title = {Emotional Satisfaction in Color Image Retrieval},
  booktitle = {Proceedings Swedish Symposium on Image Analysis 2008},
  year = {2008},
  pages = {7--10}
}
Alsam, A. and Lenz, R. Calibrating Color Cameras using Metameric Blacks 2007 Journal Optical Society of America A
Vol. 24(1), pp. 11-17 
article  
Abstract: Spectral calibration of digital cameras based on the spectral data of commercially available calibration charts is an ill-conditioned problem that has an infinite number of solutions. We introduce a method to estimate the sensor's spectral sensitivity function based on metamers. For a given patch on the calibration chart we construct numerical metamers by computing convex linear combinations of spectra from calibration chips with lower and higher sensor response values. The difference between the measured reflectance spectrum and the numerical metamer lies in the null space of the sensor. For each measured spectrum we use this procedure to compute a collection of color signals that lie in the null space of the sensor. For a collection of such spaces we compute the robust principal components, and we obtain an estimate of the sensor by computing the common null space spanned by these vectors. Our approach has a number of advantages over standard techniques: It is robust to outliers and is not dominated by larger response values, and it offers the ability to evaluate the goodness of the solution where it is possible to show that the solution is optimal, given the data, if the calculated range is one dimensional.
BibTeX:
@article{Alsam2007,
  author = {Ali Alsam and Reiner Lenz},
  title = {Calibrating Color Cameras using Metameric Blacks},
  journal = {Journal Optical Society of America A},
  year = {2007},
  volume = {24},
  number = {1},
  pages = {11--17}
}
Latorre Carmona, P. and Lenz, R. Performance evaluation of dimensionality reduction techniques for multispectral images 2007 Int. J. Imaging Systems and Technology
Vol. 17(3), pp. 202-217 
article DOI  
Abstract: We consider several collections of multispectral color signals and describe how linear and nonlinear methods can be used to investigate their internal structure. We use databases consisting of blackbody radiators, approximated and measured daylight spectra, multispectral images of indoor and outdoor scenes under different illumination conditions, and numerically computed color signals. We apply principal components analysis, group-theoretical methods and three manifold learning methods: Laplacian Eigenmaps, ISOMAP, and conformal component analysis. Identification of low-dimensional structures in these databases is important for analysis, model building and compression and we compare the results obtained by applying the algorithms to the different databases.
BibTeX:
@article{LatorreCarmona2007,
  author = {Latorre Carmona, Pedro and Reiner Lenz},
  title = {Performance evaluation of dimensionality reduction techniques for multispectral images},
  journal = {Int. J. Imaging Systems and Technology},
  year = {2007},
  volume = {17},
  number = {3},
  pages = {202--217},
  doi = {http://doi.org/10.1002/ima.20107}
}
Latorre Carmona, P., Lenz, R., Pla, F. and Sotoca, J. Affine Illumination Compensation for Multispectral Images 2007 Image Analysis
Vol. 4522Image Analysis, 15th Scandinavian Conference, SCIA 2007, Aalborg, Denmark, June 10-14, 2007, pp. 522-531 
inproceedings URL 
Abstract: We apply a general form of affine transformation model to compensate illumination variations in a series of multispectral images of a static scene and compare it to a particular affine and a diagonal transformation models. These models operate in the original multispectral space or in a lower-dimensional space obtained by Singular Value Decomposition (SVD) of the set of images. We use a system consisting of a multispectral camera and a light dome that allows the measurement of multispectral data under carefully controlled illumination conditions to generate a series of multispectral images of a static scene under varying illumination conditions. We evaluate the compensation performance using the CIELAB colour difference between images. The experiments show that the first 2 models perform satisfactorily in the original and lower dimensional spaces.
BibTeX:
@inproceedings{LatorreCarmona2007a,
  author = {Latorre Carmona, Pedro and Lenz, Reiner and Pla, Filiberto and Sotoca, Jose},
  title = {Affine Illumination Compensation for Multispectral Images},
  booktitle = {Image Analysis, 15th Scandinavian Conference, SCIA 2007, Aalborg, Denmark, June 10-14, 2007},
  journal = {Image Analysis},
  publisher = {Springer},
  year = {2007},
  volume = {4522},
  pages = {522--531},
  url = {http://dx.doi.org/10.1007/978-3-540-73040-8_53}
}
Lenz, R. Crystal vision-applications of point groups in computer vision 2007
Vol. 4844,Proc. Asian Conference Computer Vision ACCV 2007, pp. 744-753 
inproceedings  
Abstract: We use methods from the representation theory of finite groups to construct efficient processing methods for the special geometries related to the finite subgroups of the rotation group. We motivate the use of these subgroups in computer vision, summarize the necessary facts from the representation theory and develop the basics of Fourier theory for these geometries. We illustrate its usage for data compression in applications where the processes are (on average) symmetrical with respect to these groups. We use the icosahedral group as an example since it is the largest finite subgroup of the 3D rotation group. Other subgroups with fewer group elements can be studied in exactly the same way.
BibTeX:
@inproceedings{Lenz2007,
  author = {Reiner Lenz},
  title = {Crystal vision-applications of point groups in computer vision},
  booktitle = {Proc. Asian Conference Computer Vision ACCV 2007},
  publisher = {Springer},
  year = {2007},
  volume = {4844,},
  pages = {744--753}
}
Lenz, R. Optimizing Color 2007 Proceedings of the Second International Workshop on Image Media Quality and its Applications, pp. 64-69  inproceedings  
Abstract: Non-negative color signals are all located in a conical section of a function space. We use the geometrical properties of this conical space to describe chromaticity changes by differential equations related to the Lorentz group SU(1,1). After a short summary of the necessary mathematical background we illustrate the properties of this model using multichannel images of natural scenes and black body illuminants of different temperatures. We show how the parameters of the differential equations can be extracted from multispectral and RGB measurements. We illustrate the application of the model by showing how to compress highdimensional multispectral data, how to compensate illumination changes and how to simulate the effects of illumination changes.
BibTeX:
@inproceedings{Lenz2007b,
  author = {Reiner Lenz},
  title = {Optimizing Color},
  booktitle = {Proceedings of the Second International Workshop on Image Media Quality and its Applications},
  year = {2007},
  pages = {64--69},
  note = {ISBN 4-9902707-2-X C3855}
}
Lenz, R., Latorre Carmona, P. and Meer, P. The Hyperbolic Geometry of Illumination-Induced Chromaticity Changes 2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007. CVPR '07., pp. 1-6  inproceedings DOI  
Abstract: The non-negativity of color signals implies that they span a conical space with a hyperbolic geometry. We use perspective projections to separate intensity from chromaticity, and for 3-D color descriptors the chromatic properties are represented by points on the unit disk. Descriptors derived from the same object point but under different imaging conditions can be joined by a hyperbolic geodesic. The properties of this model are investigated using multichannel images of natural scenes and black body illuminants of different temperatures. We show, over a series of static scenes with different illuminants, how illumination changes influence the hyperbolic distances and the geodesics. Descriptors derived from conventional RGB images are also addressed.
BibTeX:
@inproceedings{Lenz2007a,
  author = {Lenz, Reiner and Latorre Carmona, Pedro and Meer, Peter},
  title = {The Hyperbolic Geometry of Illumination-Induced Chromaticity Changes},
  booktitle = {IEEE Conference on Computer Vision and Pattern Recognition, 2007. CVPR '07.},
  year = {2007},
  pages = {1--6},
  doi = {http://doi.org/10.1109/CVPR.2007.383212}
}
Solli, M. and Lenz, R. FyFont: Find-your-Font in Large Font Databases 2007 Image Analysis
Vol. 4522Image Analysis, 15th Scandinavian Conference, SCIA 2007, Aalborg, Denmark, June 10-14, 2007, pp. 432-441 
inproceedings URL 
Abstract: A search engine for font recognition in very large font data-bases is presented and evaluated. The search engine analyzes an image of a text line, and responds with the name of the font used when writing the text. After segmenting the input image into single characters, the recognition is mainly based on eigenimages calculated from edge filtered character images. We evaluate the system with printed and scanned text lines and character images. The database used contains 2763 different fonts from the English alphabet. Our evaluation shows that for 99.8 % of the queries, the correct font name is one of the five best matches. Apart from finding fonts in large databases, the search engine can also be used as a pre-processor for Optical Character Recognition.
BibTeX:
@inproceedings{Solli2007,
  author = {Solli, Martin and Lenz, Reiner},
  title = {FyFont: Find-your-Font in Large Font Databases},
  booktitle = {Image Analysis, 15th Scandinavian Conference, SCIA 2007, Aalborg, Denmark, June 10-14, 2007},
  journal = {Image Analysis},
  publisher = {Springer},
  year = {2007},
  volume = {4522},
  pages = {432--441},
  url = {http://dx.doi.org/10.1007/978-3-540-73040-8_44}
}
Solli, M. and Lenz, R. HOW TO FIND THE FONT NAME FOR THIS TITLE 2007 Proc. Swedish Symposium in Image Analysis, pp. 37-40  inproceedings  
BibTeX:
@inproceedings{Solli2007a,
  author = {Martin Solli and Reiner Lenz},
  title = {HOW TO FIND THE FONT NAME FOR THIS TITLE},
  booktitle = {Proc. Swedish Symposium in Image Analysis},
  year = {2007},
  pages = {37--40}
}
Alsam, A. and Lenz, R. Calibrating Color Cameras Using Metameric Blacks 2006 Proc. Third European Conference on Color in Graphics, Imaging and Vision, pp. 75-80  inproceedings  
Abstract: Spectral calibration of digital cameras based on the spectral data of commercially available calibration charts is an illconditioned problem which has an infinite number of solutions. To improve upon the estimate, different constraints are commonly employed. Traditionally such constraints include: nonnegativity, smoothness, uni-modality and that the estimated sensors results in as good as possible response fit. In this paper, we introduce a novel method to solve a general ill-conditioned linear system with special focus on the solution of spectral calibration. We introduce a new approach based on metamerism. We observe that the difference between two metamers (spectra that integrate to the same sensor response) is in the null-space of the sensor. These metamers are used to robustly estimate the sensorï¿?s null-space. Based on this nullspace, we derive projection operators to solve for the range of the unknown sensor. Our new approach has a number of advantages over standard techniques: It involves no minimization which means that the solution is robust to outliers and is not dominated by larger response values. It also offers the ability to evaluate the goodness of the solution where it is possible to show that the solution is optimal, given the data, if the calculated range is one dimensional. When comparing the new algorithm with the truncated singular value decomposition and Tikhonov regularization we found that the new method performs slightly better for the training set with noticeable improvements for the test data.
BibTeX:
@inproceedings{Alsam2006,
  author = {Ali Alsam and Reiner Lenz},
  title = {Calibrating Color Cameras Using Metameric Blacks},
  booktitle = {Proc. Third European Conference on Color in Graphics, Imaging and Vision},
  publisher = {IS&T: The Society for Imaging Science and Technology,},
  year = {2006},
  pages = {75--80},
  note = {Leeds, UK}
}
Bui, T., Lenz, R. and Solli, M. Illumination Induced Changes in Image Statistics 2006 Proc. Third European Conference on Color in Graphics, Imaging and Vision, pp. 48-53  inproceedings  
Abstract: We have previously shown that it is possible to construct a coordinate system in the space of illumination spectra such that the coordinate vectors of the illuminants are located in a cone. Changes in the space of illuminants can then be described by an intensity related scaling and a transformation in the Lorentz group SU(1,1). In practice it is often difficult and expensive to measure these coordinate vectors. Therefore it is of interest to estimate the characteristics of an illuminant from an RGB image captured by a camera. In this paper we will investigate the relation between sequences of illuminants and statistics computed from RGB images of scenes illuminated by these illuminants. As a typical example we will study sequences of black body radiators of varying temperature. We have shown earlier that black body radiators in the mired parametrization can be described by one-parameter groups of the Lorentz group SU(1,1). In this paper we will show that this group theoretical structure of the illuminant space induces a similar structure in spaces of statistical descriptors of the resulting RGB images. We show this relation for mean vectors of RGB images, for RGB histograms and for histograms of images obtained by applying certain spatiospectral linear filters to the RGB images. As a result we obtain estimates of the color temperature of the illuminant from sequences of RGB images of scenes under these illuminants.
BibTeX:
@inproceedings{Bui2006,
  author = {Thanh Bui and Reiner Lenz and Martin Solli},
  title = {Illumination Induced Changes in Image Statistics},
  booktitle = {Proc. Third European Conference on Color in Graphics, Imaging and Vision},
  publisher = {IS&T: The Society for Imaging Science and Technology, Springfield, VA 22151 USA},
  year = {2006},
  pages = {48--53},
  note = {Leeds, UK}
}
Lenz, R. and Solli, M. Lie Methods in Color Signal Processing: Illumination Effects 2006
Vol. IIIProc. ICPR 2006,Hongkong, pp. 738-741 
inproceedings URL 
BibTeX:
@inproceedings{Lenz2006,
  author = {R. Lenz and M. Solli},
  title = {Lie Methods in Color Signal Processing: Illumination Effects},
  booktitle = {Proc. ICPR 2006,Hongkong},
  publisher = {IEEE-Press},
  year = {2006},
  volume = {III},
  pages = {738--741},
  url = {http://webstaff.itn.liu.se/ reile/prints/icpr-2006.pdf}
}
Bui, T.H. Group-Theoretical Structure in Multispectral Color and Image Databases 2005 Linköping studies in science and technology. Dissertations, ISSN 0345-7524 ; 962, pp. 1-193School: Linköping University  phdthesis URL 
Abstract: Many applications lead to signals with nonnegative function values. Understanding the structure of the spaces of nonnegative signals is therefore of interest in many different areas. Hence, constructing effective representation spaces with suitable metrics and natural transformations is an important research topic. In this thesis, we present our investigations of the structure of spaces of nonnegative signals and illustrate the results with applications in the fields of multispectral color science and content-based image retrieval. The infinite-dimensional Hilbert space of nonnegative signals is conical and convex. These two properties are preserved under linear projections onto lower dimensional spaces. The conical nature of these coordinate vector spaces suggests the use of hyperbolic geometry. The special case of three-dimensional hyperbolic geometry leads to the application of the SU(1,1) or SO 2,1) groups. We introduce a new framework to investigate nonnegative signals. We use PCA-based coordinates and apply group theoretical tools to investigate sequences of signal coordinate vectors. We describe these sequences with oneparameter subgroups of SU(1,1) and show how to compute the one-parameter subgroup of SU(1,1) from a given set of nonnegative signals. In our experiments we investigate the following signal sequences: (i) blackbody radiation spectra; (ii) sequences of daylight/twilight spectra measured in Norrkï¿?oping, Sweden and in Granada, Spain; (iii) spectra generated by the SMARTS2 simulation program; and (iv) sequences of image histograms. The results show that important properties of these sequences can be modeled in this framework. We illustrate the usefulness with examples where we derive illumination invariants and introduce an efficient visualization implementation. Content-Based Image Retrieval (CBIR) is another topic of the thesis. In such retrieval systems, images are first characterized by descriptor vectors. Retrieval is then based on these content-based descriptors. Selection of contentbased descriptors and defining suitable metrics are the core of any CBIR system. We introduce new descriptors derived by using group theoretical tools. We exploit the symmetry structure of the space of image patches and use the group theoretical methods to derive low-level image filters in a very general framework. The derived filters are simple and can be used for multispectral images and images defined on different sampling grids. These group theoretical filters are then used to derive content-based descriptors, which will be used in a real implementation of a CBIR.
BibTeX:
@phdthesis{Bui2005a,
  author = {Thanh Hai Bui},
  title = {Group-Theoretical Structure in Multispectral Color and Image Databases},
  booktitle = {Linköping studies in science and technology. Dissertations, ISSN 0345-7524 ; 962},
  publisher = {Linköping University, Department of Science and Technology},
  school = {Linköping University},
  year = {2005},
  pages = {1--193},
  url = {http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-3818}
}
Bui, T.H., Lenz, R. and Kruse, B. Color and Texture Induced Structures of Keyword Space 2005
Vol. 2Proceedings. of 10th Congress of the International Colour Association, pp. 1059-1062 
inproceedings  
BibTeX:
@inproceedings{Bui2005,
  author = {Thanh Hai Bui and Reiner Lenz and Björn Kruse},
  title = {Color and Texture Induced Structures of Keyword Space},
  booktitle = {Proceedings. of 10th Congress of the International Colour Association},
  year = {2005},
  volume = {2},
  pages = {1059--1062}
}
Lenz, R. Spectral Color Spaces: Their Structure and Transformations 2005
Vol. 138Advances in imaging and electron physics, pp. 1-67 
incollection URL 
BibTeX:
@incollection{Lenz2005b,
  author = {Reiner Lenz},
  title = {Spectral Color Spaces: Their Structure and Transformations},
  booktitle = {Advances in imaging and electron physics},
  publisher = {Elsevier},
  year = {2005},
  volume = {138},
  pages = {1--67},
  url = {http://webstaff.itn.liu.se/ reile/prints/aiep.pdf}
}
Lenz, R. and Bui, T. Statistical properties of color-signal spaces 2005 Journal of the Optical Society of America A (Optics, Image Science and Vision)
Vol. 22(5)J. Opt. Soc. Am. A, Opt. Image Sci. Vis. (USA), pp. 820-7 
article URL 
Abstract: In applications of principal component analysis (PCA) it has often been observed that the eigenvector with the largest eigenvalue has only nonnegative entries when the vectors of the underlying stochastic process have only nonnegative values. This has been used to show that the coordinate vectors in PCA are all located in a cone. We prove that the nonnegativity of the first eigenvector follows from the Perron-Frobenius (and Krein-Rutman theory). Experiments show also that for stochastic processes with nonnegative signals the mean vector is often very similar to the first eigenvector. This is not true in general, but we first give a heuristical explanation why we can expect such a similarity. We then derive a connection between the dominance of the first eigenvalue and the similarity between the mean and the first eigenvector and show how to check the relative size of the first eigenvalue without actually computing it. In the last part of the paper we discuss the implication of theoretical results for multispectral color processing
BibTeX:
@article{Lenz2005d,
  author = {Lenz, R. and Bui, T.H.},
  title = {Statistical properties of color-signal spaces},
  booktitle = {J. Opt. Soc. Am. A, Opt. Image Sci. Vis. (USA)},
  journal = {Journal of the Optical Society of America A (Optics, Image Science and Vision)},
  publisher = {Opt. Soc. America},
  year = {2005},
  volume = {22},
  number = {5},
  pages = {820--7},
  url = {http://webstaff.itn.liu.se/ reile/prints/josaa-2005.pdf}
}
Lenz, R., Bui, T.H. and Takase, K. A Group Theoretical Toolbox for Color Image Operators 2005
Vol. IIIProc. ICIP 05, pp. 557-560 
inproceedings  
BibTeX:
@inproceedings{Lenz2005,
  author = {Reiner Lenz and Thanh Hai Bui and Koichi Takase},
  title = {A Group Theoretical Toolbox for Color Image Operators},
  booktitle = {Proc. ICIP 05},
  year = {2005},
  volume = {III},
  pages = {557--560}
}
Lenz, R., Bui, T.H. and Takase, K. Fast Low-Level Filter Systems for Multispectral Color Images 2005
Vol. 1Proceedings. of 10th Congress of the International Colour Association, pp. 535-538 
inproceedings  
BibTeX:
@inproceedings{Lenz2005a,
  author = {Reiner Lenz and Thanh Hai Bui and Koichi Takase},
  title = {Fast Low-Level Filter Systems for Multispectral Color Images},
  booktitle = {Proceedings. of 10th Congress of the International Colour Association},
  year = {2005},
  volume = {1},
  pages = {535--538}
}
Lenz, R., Hai Bui, T. and Hernandez-Andres, J. Group Theoretical Structure of Spectral Spaces 2005 Journal of Mathematical Imaging and Vision
Vol. 23(3), pp. 297-313 
article URL 
BibTeX:
@article{Lenz2005c,
  author = {Lenz, Reiner and Hai Bui, Thanh and Hernandez-Andres, Javier},
  title = {Group Theoretical Structure of Spectral Spaces},
  journal = {Journal of Mathematical Imaging and Vision},
  year = {2005},
  volume = {23},
  number = {3},
  pages = {297--313},
  url = {http://webstaff.itn.liu.se/ reile/prints/jmiv-2005.pdf}
}
Solli, M., Andersson, M., Kruse, B. and Lenz, R. Digital Camera Characterization for Color Measurements 2005 2005 Beijing International Conference on Imaging: Technology and Applications for the 21st Century, pp. 278-279  inproceedings  
BibTeX:
@inproceedings{Solli2005,
  author = {Martin Solli and Mattias Andersson and Björn Kruse and Reiner Lenz},
  title = {Digital Camera Characterization for Color Measurements},
  booktitle = {2005 Beijing International Conference on Imaging: Technology and Applications for the 21st Century},
  publisher = {Science Press},
  year = {2005},
  pages = {278--279}
}
Solli, M., Andersson, M., Lenz, R. and Kruse, B. Color Measurements with a Consumer Digital Camera Using Spectral Estimation Techniques 2005
Vol. 3540Proc. Scandinavian Conference Image Analysis 2005, pp. 105-114 
inproceedings URL 
Abstract: The use of spectrophotometers for color measurements on printed substrates is widely spread among paper producers as well as within the printing industry. Spectrophotometer measurements are precise, but time-consuming procedures and faster methods are desirable. The rapid development of digital cameras has opened the possibility to use consumer digital cameras as substitutes for spectrophotometers for certain applications such as production control. Two methods for estimating the reflectance properties of objects from camera RGB measurements using linear estimation techniques combined with linear and non-linear constraints are presented. In the experiments, we have investigated if these techniques can be used to measure the reflectance properties of flat objects such as printed pages of paper. Reflectances were converted to CIELAB color values, and the minimization of color errors were evaluated with CIE color difference formulas. Our experiments show that a consumer digital camera can be used as a fast and inexpensive alternative to spectrophotometers for color measurements on printed substrates.
BibTeX:
@inproceedings{Solli2005a,
  author = {Martin Solli and Mattias Andersson and Reiner Lenz and Björn Kruse},
  title = {Color Measurements with a Consumer Digital Camera Using Spectral Estimation Techniques},
  booktitle = {Proc. Scandinavian Conference Image Analysis 2005},
  publisher = {Springer Verlag},
  year = {2005},
  volume = {3540},
  pages = {105--114},
  url = {http://webstaff.itn.liu.se/ reile/prints/scia-2005.pdf}
}
Tran, L.V. and Lenz, R. Compact colour descriptors for colour-based image retrieval 2005 Signal Processing
Vol. 85(2), pp. 233-246 
article URL 
Abstract: In many colour-based image retrieval systems the colour properties of an image are described by its colour histogram. Histogram-based search is, however, often inefficient for large histogram sizes. Therefore we introduce several new, Karhunen-Loeve transform (KLT)-based methods that provide efficient representations of colour histograms and differences between two colour histograms. The methods are based on the following two observations; Ordinary KLT considers colour histograms as signals and uses the Euclidian distance for optimization; KLT with generalized colour distance measures that take into account both the statistical properties of the image database and the properties of the underlying colour space should improve the retrieval performance. Image retrieval applications compare similarities between different images. Relevant for the decision is only the local structure of the image space around the current query image since the task is to find those images in the database that are most similar to this given query image. Therefore only the local topology of the feature space is of interest and compression methods should preserve this local topology as much as possible. It is therefore more important to have a good representation of the differences between features of similar images than good representations of the features of the images themselves. The optimization should therefore be based on minimizing the approximation error in the space of local histogram differences instead of the space of colour histograms. In this paper we report the results of our experiments that are done on three image databases containing more than 130,000 images. Both objective and subjective ground truth queries are used in order to evaluate the proposed methods and to compare them with other existing methods. The results from our experiments show that compression methods based on a combination of the two observations described above provide new, powerful and efficient retrieval algorithms for colour-based image retrieval.
BibTeX:
@article{Tran2005a,
  author = {Tran, Linh Viet and Lenz, Reiner},
  title = {Compact colour descriptors for colour-based image retrieval},
  journal = {Signal Processing},
  year = {2005},
  volume = {85},
  number = {2},
  pages = {233--246},
  url = {http://www.sciencedirect.com/science/article/B6V18-4DNR8GW-1/2/0a75efbfb1913e5ce2dd58a3f8f3c34f}
}
Tran, L.V. and Lenz, R. Kernel Density Estimators for Hue Based Image Retrieval 2005 Journal Imaging Science and Technology
Vol. 49(2), pp. 185-188 
article  
Abstract: Color is widely used for content-based image retrieval. In these applications the color properties of an image are characterized by the probability distribution of the colors in the image. These probability distributions are very often estimated by histograms although the histograms have many drawbacks compared to other estimators such as kernel density methods. In this article we investigate whether using kernel density estimators instead of histograms could give better retrieval results based on hue descriptors of color images. In this article we introduce the Fourier series coefficients as descriptors of hue distributions. We argue that under certain conditions these coefficients are optimal in a least squared error sense. We will also apply Parseval formula to compute the similarity of two distributions directly from these Fourier coefficients. Our experiments show that this modification of the kernel based similarity estimation has better retrieval performance than the histogram methods and we will also show that the method is insensitive to parameter changes as long as they are selected in a reasonable range.
BibTeX:
@article{Tran2005,
  author = {Linh Viet Tran and Reiner Lenz},
  title = {Kernel Density Estimators for Hue Based Image Retrieval},
  journal = {Journal Imaging Science and Technology},
  year = {2005},
  volume = {49},
  number = {2},
  pages = {185--188}
}
Bui, T.H., Lenz, R. and Landelius, T. Group theoretical investigations of daylight spectra 2004 CGIV 2004: The Second European Conference on Colour Graphics, Imaging and Vision, pp. 437-442  inproceedings  
BibTeX:
@inproceedings{Bui2004,
  author = {Bui, Thanh Hai and Lenz, Reiner and Landelius, Tomas},
  title = {Group theoretical investigations of daylight spectra},
  booktitle = {CGIV 2004: The Second European Conference on Colour Graphics, Imaging and Vision},
  publisher = {IS&T},
  year = {2004},
  pages = {437--442}
}
Lenz, R. Color Signal Processing 2004 Den 13. Danske Konference i Mï¿?nstergenkendelse og Billedanalyse, pp. 2-12  inproceedings  
BibTeX:
@inproceedings{Lenz2004b,
  author = {Lenz, Reiner},
  title = {Color Signal Processing},
  booktitle = {Den 13. Danske Konference i Mï¿?nstergenkendelse og Billedanalyse},
  publisher = {Datalogisk Institut, Universitetsparken 1, DK-2100 Copenhagen, Denmark http://www.diku.dk/publikationer/tekniske.rapporter/2004/},
  year = {2004},
  pages = {2--12}
}
Lenz, R. Time-Frequency Analysis of Color Spectra 2004 CGIV 2004: The Second European Conference on Colour Graphics, Imaging and Vision, pp. 499-504  inproceedings  
BibTeX:
@inproceedings{Lenz2004,
  author = {Lenz, Reiner},
  title = {Time-Frequency Analysis of Color Spectra},
  booktitle = {CGIV 2004: The Second European Conference on Colour Graphics, Imaging and Vision},
  publisher = {IS&T},
  year = {2004},
  pages = {499--504}
}
Lenz, R. and Bui, T. Recognition of non-negative patterns 2004
Vol. Vol.3Proceedings of the 17th International Conference on Pattern Recognition, pp. 498-501 
inproceedings  
Abstract: Principal component analysis (PCA) is one of the most important and popular tools used to recognize and compress patterns. The principal components are the basis functions that minimize the mean-squared error and they can be used as matched filters. In many PCA applications it has been observed that the eigenvector with the largest eigenvalue has only non-negative entries when the vectors of the underlying stochastic process have only non-negative values. This has been used to show that the coordinate vectors in PCA are all located in a cone. This in turn can be used to construct invariants, for tracking or compression. In this paper we show how this empirical observation can be rigorously proved. For the case of patterns described by vectors we use the Perron-Frobenius theory of non-negative matrices to investigate stochastic processes of finite-dimensional patterns that assume only non-negative function values. We show that they always have a first eigenfunction that assumes only non-negative values. We also describe the conditions under which the first eigenfunction has strictly positive values. For stochastic processes of patterns in Hilbert (or Banach) spaces we use versions of the Krein-Rutman theory to prove the non-negativity of the first eigenfunction. In contrast to the finite-dimensional case we see that this formulation gives a more direct connection to the conical structure of the underlying pattern space. As a concrete example we sketch how these results can be used in multi-spectral color processing
BibTeX:
@inproceedings{Lenz2004c,
  author = {Lenz, R. and Bui, T.H.},
  title = {Recognition of non-negative patterns},
  booktitle = {Proceedings of the 17th International Conference on Pattern Recognition},
  publisher = {IEEE Comput. Soc},
  year = {2004},
  volume = {Vol.3},
  pages = {498--501}
}
Lenz, R. and Hernandez-Andres, J. Time-Frequency Analysis for Multi-Channel Color Pattern Recognition 2004 CGIV 2004: The Second European Conference on Colour Graphics, Imaging and Vision, pp. 509-514  inproceedings  
BibTeX:
@inproceedings{Lenz2004a,
  author = {Reiner Lenz and Javier Hernandez-Andres},
  title = {Time-Frequency Analysis for Multi-Channel Color Pattern Recognition},
  booktitle = {CGIV 2004: The Second European Conference on Colour Graphics, Imaging and Vision},
  publisher = {IS&T},
  year = {2004},
  pages = {509--514}
}
Olsson, B., Ynnerman, A. and Lenz, R. Computing synthetic satellite images from weather prediction data 2004 Proc. SPIE-2004, Visualization and Data Analysis 2004, San Jose, USA  inproceedings  
BibTeX:
@inproceedings{Olsson2004a,
  author = {B. Olsson and A. Ynnerman and R. Lenz},
  title = {Computing synthetic satellite images from weather prediction data},
  booktitle = {Proc. SPIE-2004, Visualization and Data Analysis 2004, San Jose, USA},
  year = {2004}
}
Olsson, B., Ynnerman, A. and Lenz, R. Visualizing weather with synthetic high dynamic range images 2004 Proc. SPIE-2004, Visualization and Data Analysis 2004, San Jose, USA  inproceedings  
BibTeX:
@inproceedings{Olsson2004,
  author = {B. Olsson and A. Ynnerman and R. Lenz},
  title = {Visualizing weather with synthetic high dynamic range images},
  booktitle = {Proc. SPIE-2004, Visualization and Data Analysis 2004, San Jose, USA},
  year = {2004}
}
Tran, L.V. and Lenz, R. Efficient Descriptors of Hue Distributions from Kernel Density Estimators and Fourier Transforms 2004 CGIV 2004: The Second European Conference on Colour Graphics, Imaging and Vision, pp. 151-155  inproceedings  
BibTeX:
@inproceedings{Tran2004,
  author = {Linh Viet Tran and Reiner Lenz},
  title = {Efficient Descriptors of Hue Distributions from Kernel Density Estimators and Fourier Transforms},
  booktitle = {CGIV 2004: The Second European Conference on Colour Graphics, Imaging and Vision},
  publisher = {IS&T},
  year = {2004},
  pages = {151--155}
}
Bui, T.H. Non-Euclidean structures in PCA-based descriptions of multispectral databases 2003 School: Linköping University  phdthesis  
BibTeX:
@phdthesis{Bui2003,
  author = {Thanh Hai Bui},
  title = {Non-Euclidean structures in PCA-based descriptions of multispectral databases},
  school = {Linköping University},
  year = {2003},
  note = {ISBN/ISSN: 9173737666}
}
Lenz, R., Bui, T. and Hernandez-Andres, J. One-parameter subgroups and the chromaticity properties of time-changing illumination spectra 2003
Vol. 5008Proc. SPIE - Int. Soc. Opt. Eng. (USA), pp. 237-48 
inproceedings  
Abstract: Understanding the properties of time-varying illumination spectra is of importance in all applications where dynamical color changes due to changes in illumination characteristics have to be analyzed or synthesized. Examples are (dynamical) color constancy and the creation of realistic animations. We show how group theoretical methods can be used to describe sequences of time changing illumination spectra with only few parameters. From the description we can also derive a differential equation that describes the illumination changes. We illustrate the method with investigations of black-body radiation and measured sequences of daylight spectra
BibTeX:
@inproceedings{Lenz2003b,
  author = {Lenz, R. and Bui, T.H. and Hernandez-Andres, J.},
  title = {One-parameter subgroups and the chromaticity properties of time-changing illumination spectra},
  booktitle = {Proc. SPIE - Int. Soc. Opt. Eng. (USA)},
  publisher = {SPIE-Int. Soc. Opt. Eng},
  year = {2003},
  volume = {5008},
  pages = {237--48}
}
Lenz, R. and Bui, T.H. Efficient Descriptors of Hue Distributions from Kernel Density Estimators and Fourier Transforms 2003 Proc. Swedish Society for Automated Image Analysis  inproceedings  
BibTeX:
@inproceedings{Lenz2003a,
  author = {Reiner Lenz and Thanh Hai Bui},
  title = {Efficient Descriptors of Hue Distributions from Kernel Density Estimators and Fourier Transforms},
  booktitle = {Proc. Swedish Society for Automated Image Analysis},
  year = {2003}
}
Lenz, R. and Bui, T.H. Illumination Invariants 2003 Proc. PICS-2003, pp. 506-511  inproceedings  
BibTeX:
@inproceedings{Lenz2003c,
  author = {Reiner Lenz and Thanh Hai Bui},
  title = {Illumination Invariants},
  booktitle = {Proc. PICS-2003},
  year = {2003},
  pages = {506--511}
}
Lenz, R., Tran, L.V. and Bui, T.H. Group Theoretical Invariants in Color Image Processing 2003 Proc. Eleventh Color Imaging Conference, pp. 212-217  inproceedings  
BibTeX:
@inproceedings{Lenz2003,
  author = {Reiner Lenz and Linh Viet Tran and Thanh Hai Bui},
  title = {Group Theoretical Invariants in Color Image Processing},
  booktitle = {Proc. Eleventh Color Imaging Conference},
  year = {2003},
  pages = {212--217}
}
Olsson, B., Ynnerman, A. and Lenz, R. Eigenskies: a method of visualizing weather prediction data 2003
Vol. 5009Proc. SPIE - Int. Soc. Opt. Eng. (USA), pp. 1-10 
inproceedings  
Abstract: Visualizing a weather prediction data set by actually synthesizing an image of the sky is a difficult problem. In this paper we present a method for synthesizing realistic sky images from weather prediction and climate prediction data. Images of the sky are combined with a number of weather parameters (like pressure and temperature) to train an artificial neural network (ANN) to predict the appearance of the sky from certain weather parameters. Hourly measurements from a period of eight months are used. The principal component analysis (PCA) method is used to decompose images of the sky into their eigen components - the eigenskies. In this way the image information is compressed into a small number of coefficients while still preserving the main information in the image. This means that the fine details of the cloud cover cannot be synthesized using this method. The PCA coefficients together with measured weather parameters at the same time form a data point that is used to train the ANN. The results show that the method gives adequate results and although some discrepancies exist, the main appearance is correct. It is possible to distinguish between different types of weather. A rainy day looks rainy and a sunny day looks sunny
BibTeX:
@inproceedings{Olsson2003a,
  author = {Olsson, B. and Ynnerman, A. and Lenz, R.},
  title = {Eigenskies: a method of visualizing weather prediction data},
  booktitle = {Proc. SPIE - Int. Soc. Opt. Eng. (USA)},
  publisher = {SPIE-Int. Soc. Opt. Eng},
  year = {2003},
  volume = {5009},
  pages = {1--10}
}
Olsson, B., Ynnerman, A. and Lenz, R. SkyVis, an application of Matlab in meteorological visualization 2003 Nordic Matlab Conference, Copenhagen  inproceedings  
BibTeX:
@inproceedings{Olsson2003,
  author = {B. Olsson and A. Ynnerman and R. Lenz},
  title = {SkyVis, an application of Matlab in meteorological visualization},
  booktitle = {Nordic Matlab Conference, Copenhagen},
  year = {2003}
}
Tran, L. and Lenz, R. Characterization of color distributions with histograms and kernel density estimators 2003
Vol. 5018Proc. SPIE - Int. Soc. Opt. Eng. (USA), pp. 179-89 
inproceedings  
Abstract: Color is widely used for content-based image retrieval. In these applications the color properties of an image are characterized by the probability distribution of the colors in the image. These probability distributions are very often estimated by histograms although the histograms have many drawbacks compared to other estimators such as kernel density methods. In this paper we investigate whether using kernel density estimators instead of histograms could give better descriptors of color images. Experiments using these descriptors to estimate the parameters of the underlying color distribution and in color based image retrieval (CBIR) applications were carried out in which the MPEG71 database of 5466 color images with 50 standard queries are used as the benchmark. Noisy images are also generated and put into the CBIR application to test the robustness of the descriptors against the noise. The results of our experiments show that good density estimators are not necessarily good descriptors for CBIR applications. We found that the histograms perform better than kernel based methods when used as descriptors for CBIR applications. In the second part of the paper, optimal values of important parameters in the construction of these descriptors, particularly the smoothing parameters or the bandwidth of the estimators, are discussed. Our experiments show that using over-smoothed bandwidth gives better retrieval performance
BibTeX:
@inproceedings{Tran2003,
  author = {Tran, L.V. and Lenz, R.},
  title = {Characterization of color distributions with histograms and kernel density estimators},
  booktitle = {Proc. SPIE - Int. Soc. Opt. Eng. (USA)},
  publisher = {SPIE-Int. Soc. Opt. Eng},
  year = {2003},
  volume = {5018},
  pages = {179--89}
}
Tran, L. and Lenz, R. Geometric invariance in describing color features 2003
Vol. 5008Proc. SPIE - Int. Soc. Opt. Eng. (USA), pp. 101-8 
inproceedings  
Abstract: We present a projective geometry framework for color invariants using the extended dichromatic reflection model, in which more realistic and complicated illuminations are considered. Many assumptions which have been used by other methods are relaxed in our framework. Specifically some of the proposed invariants do not require any additional assumption except the ones assumed by the extended dichromatic reflection model. By putting the color invariance into the projective geometry framework, we can generate different types of invariants and clarify the assumptions under which they are valid. Experiments are presented that illustrate the results derived within our framework
BibTeX:
@inproceedings{Tran2003a,
  author = {Tran, L.V. and Lenz, R.},
  title = {Geometric invariance in describing color features},
  booktitle = {Proc. SPIE - Int. Soc. Opt. Eng. (USA)},
  publisher = {SPIE-Int. Soc. Opt. Eng},
  year = {2003},
  volume = {5008},
  pages = {101--8}
}
Viet Tran, L. Efficient Image Retrieval with Statistical Color Descriptors 2003 , pp. 205School: Linköping University, Department of Science and Technology  phdthesis URL 
Abstract: Color has been widely used in content-based image retrieval (CBIR) applications. In such applications the color properties of an image are usually characterized by the probability distribution of the colors in the image. A distance measure is then used to measure the (dis-)similarity between images based on the descriptions of their color distributions in order to quickly find relevant images. The development and investigation of statistical methods for robust representations of such distributions, the construction of distance measures between them and their applications in efficient retrieval, browsing, and structuring of very large image databases are the main contributions of the thesis. In particular we have addressed the following problems in CBIR. Firstly, different non-parametric density estimators are used to describe color information for CBIR applications. Kernel-based methods using nonorthogonal bases together with a Gram-Schmidt procedure and the application of the Fourier transform are introduced and compared to previously used histogram-based methods. Our experiments show that efficient use of kernel density estimators improves the retrieval performance of CBIR. The practical problem of how to choose an optimal smoothing parameter for such density estimators as well as the selection of the histogram bin-width for CBIR applications are also discussed. Distance measures between color distributions are then described in a differential geometry-based framework. This allows the incorporation of geometrical features of the underlying color space into the distance measure between the probability distributions. The general framework is illustrated with two examples: Normal distributions and linear representations of distributions. The linear representation of color distributions is then used to derive new compact descriptors for color-based image retrieval. These descriptors are based on the combination of two ideas: Incorporating information from the structure of the color space with information from images and application of projection methods in the space of color distribution and the space of differences between neighboring color distributions. In our experiments we used several image databases containing more than 1,300,000 images. The experiments show that the method developed in this thesis is very fast and that the retrieval performance chievedcompares favorably with existing methods. A CBIR system has been developed and is currently available at http://www.media.itn.liu.se/cse. We also describe color invariant descriptors that can be used to retrieve images of objects independent of geometrical factors and the illumination conditions under which these images were taken. Both statistics- and physics-based methods are proposed and examined. We investigated the interaction between light and material using different physical models and applied the theory of transformation groups to derive geometry color invariants. Using the proposed framework, we are able to construct all independent invariants for a given physical model. The dichromatic reflection model and the Kubelka-Munk model are used as examples for the framework. The proposed color invariant descriptors are then applied to both CBIR, color image segmentation, and color correction applications. In the last chapter of the thesis we describe an industrial application where different color correction methods are used to optimize the layout of a newspaper page. Note: A search engine based, on the methodes discribed in this thesis, can be found at http://pub.ep.liu.se/cse/db/?. Note that the question mark must be included in the address.
BibTeX:
@phdthesis{VietTran2003,
  author = {Viet Tran, Linh},
  title = {Efficient Image Retrieval with Statistical Color Descriptors},
  school = {Linköping University, Department of Science and Technology},
  year = {2003},
  pages = {205},
  url = {http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5002}
}
Fayyazi, A. and Lenz, R. Texture based Duplex-Board Layer Segmentation 2002 Proc. Swedish Society for Automated Image Analysis  inproceedings  
BibTeX:
@inproceedings{Fayyazi2002,
  author = {A. Fayyazi and R. Lenz},
  title = {Texture based Duplex-Board Layer Segmentation},
  booktitle = {Proc. Swedish Society for Automated Image Analysis},
  year = {2002}
}
Lenz, R. Li(e)ght 2002 Proc. Swedish Society for Automated Image Analysis  inproceedings  
BibTeX:
@inproceedings{Lenz2002b,
  author = {R. Lenz},
  title = {Li(e)ght},
  booktitle = {Proc. Swedish Society for Automated Image Analysis},
  year = {2002}
}
Lenz, R. Spaces of Spectral Distributions and Their Natural Geometry 2002 Proc. CGIV-2002, First European Conference on Colour in Graphics, Imaging and Vision, pp. 249-254  inproceedings  
BibTeX:
@inproceedings{Lenz2002,
  author = {Reiner Lenz},
  title = {Spaces of Spectral Distributions and Their Natural Geometry},
  booktitle = {Proc. CGIV-2002, First European Conference on Colour in Graphics, Imaging and Vision},
  year = {2002},
  pages = {249--254},
  note = {(Invited)}
}
Lenz, R. Two Stage Principal Component Analysis of Color 2002 IEEE Transactions Image Processing
Vol. 11(6), pp. 630-635 
article  
BibTeX:
@article{Lenz2002a,
  author = {Reiner Lenz},
  title = {Two Stage Principal Component Analysis of Color},
  journal = {IEEE Transactions Image Processing},
  year = {2002},
  volume = {11},
  number = {6},
  pages = {630--635}
}
Tran, L. and Lenz, R. Spaces of probability distributions and their applications to color-based image database search 2002
Vol. 4421Proc. SPIE - Int. Soc. Opt. Eng. (USA), pp. 543-6 
inproceedings  
Abstract: We present a framework to compute the distance between color distributions based on differential geometry. We investigate more detailed the case when color distributions are described as linear combinations of a set of pre-computed basic functions. Experiments in our color based image retrieval system, which were done on 1000 images from Corel image database, show the advantage of our method based on the new distance measure and color descriptor
BibTeX:
@inproceedings{Tran2002a,
  author = {Tran, L.V. and Lenz, R.},
  title = {Spaces of probability distributions and their applications to color-based image database search},
  booktitle = {Proc. SPIE - Int. Soc. Opt. Eng. (USA)},
  publisher = {SPIE-Int. Soc. Opt. Eng},
  year = {2002},
  volume = {4421},
  pages = {543--6}
}
Tran, L.V. and Lenz, R. Color Invariant Features for Dielectric Materials 2002 Proc. Swedish Society for Automated Image Analysis  inproceedings  
BibTeX:
@inproceedings{Tran2002,
  author = {L. V. Tran and R. Lenz},
  title = {Color Invariant Features for Dielectric Materials},
  booktitle = {Proc. Swedish Society for Automated Image Analysis},
  year = {2002}
}
Fayyazi, A. and Lenz, R. Duplex board layer segmentation 2001 Proc. Swedish Society for Automated Image Analysis  inproceedings  
BibTeX:
@inproceedings{Fayyazi2001,
  author = {Arash Fayyazi and Reiner Lenz},
  title = {Duplex board layer segmentation },
  booktitle = {Proc. Swedish Society for Automated Image Analysis},
  year = {2001}
}
Lenz, R. A geometric foundation of Colorimetry 2001 Ninth Color Imaging Conference, pp. 46-51  inproceedings  
BibTeX:
@inproceedings{Lenz2001,
  author = {Reiner Lenz},
  title = {A geometric foundation of Colorimetry},
  booktitle = {Ninth Color Imaging Conference},
  year = {2001},
  pages = {46--51}
}
Lenz, R. Colorimetry from geometry 2001 Proc. 3rd Int. Conf. Multispectral Color Science  inproceedings  
BibTeX:
@inproceedings{Lenz2001c,
  author = {Reiner Lenz},
  title = {Colorimetry from geometry},
  booktitle = {Proc. 3rd Int. Conf. Multispectral Color Science},
  year = {2001}
}
Lenz, R. Estimation of Illumination Characteristics 2001 IEEE Transactions Image Processing
Vol. 10(7), pp. 1031-1038 
article URL 
BibTeX:
@article{Lenz2001a,
  author = {Reiner Lenz},
  title = {Estimation of Illumination Characteristics},
  journal = {IEEE Transactions Image Processing},
  year = {2001},
  volume = {10},
  number = {7},
  pages = {1031--1038},
  url = {http://webstaff.itn.liu.se/ reile/prints/ieeeip-2001.pdf}
}
Lenz, R. and Kruse, B. NFR ï¿?rsbok 2001 2001 Med färg i blicken  inbook  
BibTeX:
@inbook{Lenz2001b,
  author = {Reiner Lenz and Björn Kruse},
  title = {NFR ï¿?rsbok 2001},
  booktitle = {Med färg i blicken},
  publisher = {Swedish Science Press},
  year = {2001}
}
Toivanen, P. and Lenz, R. On distance transforms for multispectral images 2001 Proc. 3rd Int. Conf. Multispectral Color Science  inproceedings  
BibTeX:
@inproceedings{Toivanen2001,
  author = {Pekka Toivanen and Reiner Lenz},
  title = {On distance transforms for multispectral images},
  booktitle = {Proc. 3rd Int. Conf. Multispectral Color Science},
  year = {2001}
}
Toivanen, P. and Lenz, R. On the Properties of Gray-scale Distance Transforms 2001 Proc. 12th Scandinavian Conference on Image Analysis  inproceedings  
BibTeX:
@inproceedings{Toivanen2001a,
  author = {P. Toivanen and R. Lenz},
  title = {On the Properties of Gray-scale Distance Transforms},
  booktitle = {Proc. 12th Scandinavian Conference on Image Analysis},
  year = {2001}
}
Tran, L.V. and Lenz, R. Comparison of quadratic form based color indexing methods 2001 Proc. Swedish Society for Automated Image Analysis  inproceedings  
BibTeX:
@inproceedings{Tran2001a,
  author = {Linh Viet Tran and Reiner Lenz},
  title = {Comparison of quadratic form based color indexing methods},
  booktitle = {Proc. Swedish Society for Automated Image Analysis},
  year = {2001}
}
Tran, L.V. and Lenz, R. PCA-based representation of color distributions for color based image retrieval 2001 Proc. International Conference Image Processing 2001, pp. 697-700  inproceedings  
BibTeX:
@inproceedings{Tran2001,
  author = {Linh Viet Tran and Reiner Lenz},
  title = {PCA-based representation of color distributions for color based image retrieval},
  booktitle = {Proc. International Conference Image Processing 2001},
  year = {2001},
  pages = {697--700}
}
Yang, L., Lenz, R. and Kruse, B. Light scattering and ink penetration effects on tone reproduction 2001 Journal of the Optical Society of America A (Optics, Image Science and Vision)
Vol. 18(2)J. Opt. Soc. Am. A, Opt. Image Sci. Vis. (USA), pp. 360-6 
article  
Abstract: Light scattering, or the so-called Yule-Nielsen effect, and ink penetration into the substrate paper play important roles in tone reproduction. We develop a framework in which the influences of both of these effects on the reflectance and tristimulus values of a halftone sample are investigated. The properties of the paper and the ink and their bilateral interaction can be parameterized by the reflectance Rp0 of the substrate paper, the transmittance Ti of the ink layer, the parameter γ describing the ink penetration, and p¯ describing the Yule-Nielsen effect. We derive explicit expressions that relate the reflectance of the ink dots (Ri), the paper (Rp) and the halftone image (R) as functions of these parameters. We also describe the optical dot gain as a function of these parameters. We further demonstrate that ink penetration leads to a decrease in optical dot gain and that scattering in the paper results in the printed image's being viewed as more saturated in color
BibTeX:
@article{Yang2001,
  author = {Yang, Li and Lenz, R. and Kruse, B.},
  title = {Light scattering and ink penetration effects on tone reproduction},
  booktitle = {J. Opt. Soc. Am. A, Opt. Image Sci. Vis. (USA)},
  journal = {Journal of the Optical Society of America A (Optics, Image Science and Vision)},
  publisher = {Opt. Soc. America},
  year = {2001},
  volume = {18},
  number = {2},
  pages = {360--6}
}
Hauta-Kasari, M., Wenjun, W., Miyazawa, K., Toyooka, S., Lenz, R., Parkkinen, J. and Jaaskelainen, T. Computational Technique to Design Color Filters for Optical Pattern Recognition 2000
Vol. 3The 9th Finnish Artificial Intelligence Conference, STeP 2000, Espoo, Finland, pp. 151-158 
inproceedings  
BibTeX:
@inproceedings{Hauta-Kasari2000,
  author = {M. Hauta-Kasari and W. Wenjun and K. Miyazawa and S. Toyooka and R. Lenz and J. Parkkinen and T. Jaaskelainen},
  title = {Computational Technique to Design Color Filters for Optical Pattern Recognition},
  booktitle = {The 9th Finnish Artificial Intelligence Conference, STeP 2000, Espoo, Finland},
  year = {2000},
  volume = {3},
  pages = {151--158}
}
Lenz, R. Color edge detectors for conical color spaces 2000 Proc. Int. Conf. Color in Graphics an Image Processing, pp. 284-289  inproceedings  
BibTeX:
@inproceedings{Lenz2000,
  author = {Reiner Lenz},
  title = {Color edge detectors for conical color spaces},
  booktitle = {Proc. Int. Conf. Color in Graphics an Image Processing},
  year = {2000},
  pages = {284--289}
}
Lenz, R. Lie-Light tracking 2000 Proc. Norsig 2000, pp. 379-382  inproceedings  
BibTeX:
@inproceedings{Lenz2000b,
  author = {Reiner Lenz},
  title = {Lie-Light tracking},
  booktitle = {Proc. Norsig 2000},
  year = {2000},
  pages = {379--382}
}
Lenz, R. Lie-Theory and Dynamical Illumination Changes 2000 : Algebraic Frames for the Perception-Action Cycle
Vol. 1888Proc. Algebraic Frames for the Perception-Action Cycle, pp. 218-228 
inproceedings DOI URL 
Abstract: The description of the relation between the one-parameter groups of a group and the differential operators in the Lie-algebra of the group is one of the major topics in Lie-theory. In this paper we use this framework to derive a partial differential equation which describes the relation between the time-change of the spectral characteristics of the illumination source and the change of the color pixels in an image. In the first part of the paper we introduce and justify the usage of conical coordinate systems in color space. In the second part we derive the differential equation describing the illumination change and in the last part we illustrate the algorithm with some simulation examples.
BibTeX:
@inproceedings{Lenz2000a,
  author = {Lenz, Reiner},
  title = {Lie-Theory and Dynamical Illumination Changes},
  booktitle = {Proc. Algebraic Frames for the Perception-Action Cycle},
  journal = {: Algebraic Frames for the Perception-Action Cycle},
  publisher = {Springer Verlag},
  year = {2000},
  volume = {1888},
  pages = {218--228},
  url = {http://dx.doi.org/10.1007/10722492_16},
  doi = {http://doi.org/10.1007/10722492_16}
}
Lenz, R. On Color Edge Detection 2000 Proc. Image Processing, Image Quality, Image Capture Systems Conference, pp. 278-282  inproceedings  
BibTeX:
@inproceedings{Lenz2000c,
  author = {Reiner Lenz},
  title = {On Color Edge Detection},
  booktitle = {Proc. Image Processing, Image Quality, Image Capture Systems Conference},
  year = {2000},
  pages = {278--282}
}
Tran, L.V. and Lenz, R. Measuring distances between color distributions 2000 Proc. Int. Conf. Color in Graphics an Image Processing, pp. 256-260  inproceedings  
BibTeX:
@inproceedings{Tran2000a,
  author = {Linh V. Tran and Reiner Lenz},
  title = {Measuring distances between color distributions},
  booktitle = {Proc. Int. Conf. Color in Graphics an Image Processing},
  year = {2000},
  pages = {256--260}
}
Tran, L.V. and Lenz, R. Metric structures in probability spaces: applications to color based search 2000 Proc. Swedish Society for Automated Image Analysis, pp. 21-24  inproceedings  
BibTeX:
@inproceedings{Tran2000,
  author = {Linh V. Tran and Reiner Lenz},
  title = {Metric structures in probability spaces: applications to color based search},
  booktitle = {Proc. Swedish Society for Automated Image Analysis},
  year = {2000},
  pages = {21--24}
}
Yang, L., Kruse, B. and Lenz, R. A framework for describing optical dot gain and ink penetration 2000 Proc. Swedish Society for Automated Image Analysis, pp. 53-56  inproceedings  
BibTeX:
@inproceedings{Yang2000a,
  author = {Li Yang and Björn Kruse and Reiner Lenz},
  title = {A framework for describing optical dot gain and ink penetration},
  booktitle = {Proc. Swedish Society for Automated Image Analysis},
  year = {2000},
  pages = {53--56}
}
Yang, L., Kruse, B. and Lenz, R. Light Scattering and Ink Penetration Effects on Tone Reproduction 2000 Proc. Image Processing, Image Quality, Image Capture Systems Conference, pp. 225-230  inproceedings  
BibTeX:
@inproceedings{Yang2000,
  author = {Li Yang and Björn Kruse and Reiner Lenz},
  title = {Light Scattering and Ink Penetration Effects on Tone Reproduction},
  booktitle = {Proc. Image Processing, Image Quality, Image Capture Systems Conference},
  year = {2000},
  pages = {225--230}
}
Hauta-Kasari, M., Parkkinen, J., Jaaskelainen, T. and Lenz, R. Multi-spectral texture segmentation based on the spectral co-occurrence matrix 1999 Pattern Analysis and Applications
Vol. 2(4)Pattern Anal. Appl. (UK), pp. 275-84 
article  
Abstract: Multi-spectral images are becoming more common in industrial inspection tasks where the colour is used as a quality measure. In this paper we propose a spectral co-occurrence matrix-based method to analyse multi-spectral texture images, in which every pixel contains a measured colour spectrum. We first quantise the spectral domain of the multi-spectral images using the self-organising map. Next, we label the spectral domain according to the quantised spectra. In the spatial domain, we represent a multi-spectral texture using the spectral cooccurrence matrix, which we calculate from the labelled image. In the experimental part, we present the results of segmenting natural multi-spectral textures. We compare the k-nearest neighbour (k-NN) classifier and the multilayer perceptron neural network-based segmentation results of the multi-spectral and RGB colour textures
BibTeX:
@article{Hauta-Kasari1999,
  author = {Hauta-Kasari, M. and Parkkinen, J. and Jaaskelainen, T. and Lenz, R.},
  title = {Multi-spectral texture segmentation based on the spectral co-occurrence matrix},
  booktitle = {Pattern Anal. Appl. (UK)},
  journal = {Pattern Analysis and Applications},
  publisher = {Springer-Verlag},
  year = {1999},
  volume = {2},
  number = {4},
  pages = {275--84}
}
Lenz, R. and Meer, P. Non-Euclidean structure of spectral color space 1999
Vol. 3826Proc. SPIE - Int. Soc. Opt. Eng. (USA), pp. 101-12 
inproceedings  
Abstract: Color processing methods can be divided into methods based on human color vision and spectral based methods. Human vision based methods usually describe color with three parameters which are easy to interpret since they model familiar color perception processes. They share however the limitations of human color vision such as metamerism. Spectral based methods describe colors by their underlying spectra and thus do not involve human color perception. They are often used in industrial inspection and remote sensing. Most of the spectral methods employ a low dimensional (three to ten) representation of the spectra obtained from an orthogonal (usually eigenvector) expansion. While the spectral methods have solid theoretical foundation, the results obtained are often difficult to interpret. In this paper we show that for a large family of spectra the space of eigenvector coefficients has a natural cone structure. Thus we can define a natural, hyperbolic coordinate system whose coordinates are closely related to intensity, saturation and hue. The relation between the hyperbolic coordinate system and the perceptually uniform Lab color space is also shown. Defining a Fourier transform in the hyperbolic space can have applications in pattern recognition problems
BibTeX:
@inproceedings{Lenz1999c,
  author = {Lenz, R. and Meer, P.},
  title = {Non-Euclidean structure of spectral color space},
  booktitle = {Proc. SPIE - Int. Soc. Opt. Eng. (USA)},
  publisher = {SPIE-Int. Soc. Opt. Eng},
  year = {1999},
  volume = {3826},
  pages = {101--12}
}
Lenz, R., Meer, P. and Hauta-Kasari, M. Spectral-Based Illumination Estimation and Color Correction 1999 Color Research and Application
Vol. 24(2), pp. 98-111 
article  
BibTeX:
@article{Lenz1999a,
  author = {R. Lenz and P. Meer and M. Hauta-Kasari},
  title = {Spectral-Based Illumination Estimation and Color Correction},
  journal = {Color Research and Application},
  year = {1999},
  volume = {24},
  number = {2},
  pages = {98--111}
}
Lenz, R., Tran, L. and Meer, P. Moment based normalization of color images 1999 Proc. IEEE International Workshop on Multimedia Signal Processing, pp. 103-108  inproceedings  
BibTeX:
@inproceedings{Lenz1999b,
  author = {R. Lenz and L.V. Tran and P. Meer},
  title = {Moment based normalization of color images},
  booktitle = {Proc. IEEE International Workshop on Multimedia Signal Processing},
  year = {1999},
  pages = {103--108}
}
Lenz, R. and Tran, L.V. Statistical methods for automated colour normalization and colour correction 1999 Advances in Digital Printing  inproceedings  
BibTeX:
@inproceedings{Lenz1999,
  author = {R. Lenz and L. V. Tran},
  title = {Statistical methods for automated colour normalization and colour correction},
  booktitle = {Advances in Digital Printing},
  year = {1999}
}
Lenz, R. Steerable Filters and Invariant Recognition in Spacetime 1998
Vol. VProc. Int. Conf. Acc. Sp. Sig. Proc. 1998, pp. 2737-2740 
inproceedings  
BibTeX:
@inproceedings{Lenz1998a,
  author = {R. Lenz},
  title = {Steerable Filters and Invariant Recognition in Spacetime},
  booktitle = {Proc. Int. Conf. Acc. Sp. Sig. Proc. 1998},
  publisher = {IEEE Computer Society Press},
  year = {1998},
  volume = {V},
  pages = {2737--2740},
  note = {May, 12-15, 1998, Seattle, WA, USA}
}
Lenz, R. and Granlund, G. If I had a fisheye I would not need \SON{1,n} or, Is hyperbolic geometry useful in image processing? 1998 Proc. Swedish Society for Automated Image Analysis Symposium, Uppsala, Sweden, pp. 49-52  inproceedings  
BibTeX:
@inproceedings{Lenz1998c,
  author = {R. Lenz and G. Granlund},
  title = {If I had a fisheye I would not need \SON{1,n} or, Is hyperbolic geometry useful in image processing?},
  booktitle = {Proc. Swedish Society for Automated Image Analysis Symposium, Uppsala, Sweden},
  year = {1998},
  pages = {49--52}
}
Lenz, R. and Meer, P. Spectral Color Representations: Color Correction, Database Search and Maximum Entropy Printing 1998 Proc. Swedish Society for Automated Image Analysis Symposium, Uppsala, Sweden, pp. 9-12  inproceedings  
BibTeX:
@inproceedings{Lenz1998b,
  author = {R. Lenz and P. Meer},
  title = {Spectral Color Representations: Color Correction, Database Search and Maximum Entropy Printing},
  booktitle = {Proc. Swedish Society for Automated Image Analysis Symposium, Uppsala, Sweden},
  year = {1998},
  pages = {9--12}
}
Meer, P., Lenz, R. and Ramakrishna, S. Efficient invariant representations 1998 Int. J. Computer Vision
Vol. 26(2), pp. 137-152 
article URL 
BibTeX:
@article{Meer1998,
  author = {P. Meer and R. Lenz and S. Ramakrishna},
  title = {Efficient invariant representations},
  journal = {Int. J. Computer Vision},
  year = {1998},
  volume = {26},
  number = {2},
  pages = {137--152},
  url = {http://webstaff.itn.liu.se/ reile/prints/ijcv-1998.pdf}
}
Hauta-Kasari, M., Parkkinen, J., Jaaskelainen, T. and Lenz, R. Spectral based analysis of color images 1997
Vol. 2AIC Color 97, pp. 548-551 
inproceedings  
BibTeX:
@inproceedings{Hauta-Kasari1997,
  author = {M. Hauta-Kasari and J. Parkkinen and T. Jaaskelainen and R. Lenz},
  title = {Spectral based analysis of color images},
  booktitle = {AIC Color 97},
  publisher = {The Color Science Association of Japan},
  year = {1997},
  volume = {2},
  pages = {548--551}
}
Hauta-Kasari, M., Wang, W., Toyooka, S., Parkkinen, J. and Lenz, R. Unsupervised filtering of Munsell spectra 1997
Vol. 1Proc., The 3rd Asian Conference on Computer Vision,, pp. 248-255 
inproceedings  
BibTeX:
@inproceedings{Hauta-Kasari1997a,
  author = {M. Hauta-Kasari and W. Wang and S. Toyooka and J. Parkkinen and R. Lenz},
  title = {Unsupervised filtering of Munsell spectra},
  booktitle = {Proc., The 3rd Asian Conference on Computer Vision,},
  publisher = {Springer-Verlag},
  year = {1997},
  volume = {1},
  pages = {248--255}
}
Lenz, R. Some applications of representations of Lie algebras and Lie groups 1997 : Algebraic Frames for the Perception-Action Cycle
Vol. 1315/1997Algebraic Frames for the Perception-Action Cycle, pp. 114-125 
inproceedings DOI URL 
Abstract: The paper gives a short overview over some basic facts from the representation theory of groups and algebras. Then we describe iterative algorithms to normalize coefficient vectors computed by expanding functions on the unit sphere into a series of spherical harmonics. Typical applications of the normalization procedure are the matching of different three-dimensional images, orientation estimations in low-level image processing or robotics. The algorithm illustrates general methods from the representation theory of Lie-groups and Lie-algebras which can be used to linearize highly-non-linear problems. It can therefore also be adapted to applications involving groups different from the group of three-dimensional rotations. The performance of the algorithm is illustrated with a few experiments involving random coefficient vectors.
BibTeX:
@inproceedings{Lenz1997e,
  author = {Lenz, Reiner},
  title = {Some applications of representations of Lie algebras and Lie groups},
  booktitle = {Algebraic Frames for the Perception-Action Cycle},
  journal = {: Algebraic Frames for the Perception-Action Cycle},
  publisher = {Springer Verlag},
  year = {1997},
  volume = {1315/1997},
  pages = {114--125},
  url = {http://dx.doi.org/10.1007/BFb0017863},
  doi = {http://doi.org/10.1007/BFb0017857}
}
Lenz, R. and Homma, K. Constructing iterative matching algorithms with the use of Lie theory: three-dimensional orientation example 1997 Journal of the Optical Society of America A (Optics, Image Science and Vision)
Vol. 14(8)J. Opt. Soc. Am. A, Opt. Image Sci. Vis. (USA), pp. 1734-41 
article  
Abstract: Iterative algorithms are described for normalizing-coefficient vectors computed by expanding functions on the unit sphere into a series of spherical harmonics. Typical applications of the normalization procedure are the matching of different three-dimensional images, orientation estimations in low-level image processing, or robotics. The method uses general methods from the theory of Lie groups and Lie algebras to linearize the highly nonlinear original problem and can therefore also be adapted to applications involving groups different from the group of three-dimensional rotations. The performance of the algorithm is illustrated with a few experiments involving random coefficient vectors
BibTeX:
@article{Lenz1997f,
  author = {Lenz, R. and Homma, K.},
  title = {Constructing iterative matching algorithms with the use of Lie theory: three-dimensional orientation example},
  booktitle = {J. Opt. Soc. Am. A, Opt. Image Sci. Vis. (USA)},
  journal = {Journal of the Optical Society of America A (Optics, Image Science and Vision)},
  publisher = {Opt. Soc. America},
  year = {1997},
  volume = {14},
  number = {8},
  pages = {1734--41}
}
Lenz, R. and Meer, P. Color Image Normalization through Illuminant Recovery 1997 Proc. Int. Conf. Accoustics Speech and Sig. Proc. 97, pp. 3141-3144  inproceedings  
BibTeX:
@inproceedings{Lenz1997a,
  author = {R. Lenz and P. Meer},
  title = {Color Image Normalization through Illuminant Recovery},
  booktitle = {Proc. Int. Conf. Accoustics Speech and Sig. Proc. 97},
  publisher = {IEEE Computer Society Press},
  year = {1997},
  pages = {3141--3144}
}
Lenz, R., Meer, P. and Hauta-Kasari, M. Spectral-Based Illumination Estimation and Color Correction 1997 Proc. Swedish Society for Automated Image Analysis, pp. 159-163  inproceedings  
BibTeX:
@inproceedings{Lenz1997b,
  author = {R. Lenz and P. Meer and M. Hauta-Kasari},
  title = {Spectral-Based Illumination Estimation and Color Correction},
  booktitle = {Proc. Swedish Society for Automated Image Analysis},
  year = {1997},
  pages = {159--163}
}
Lenz, R., Meer, P. and Hauta-Kasari, M. Spectral-Based Illumination Estimation and Color Correction 1997 Proc. 10th Scandinavian Conference on Image Analysis, pp. 885-892  inproceedings  
BibTeX:
@inproceedings{Lenz1997c,
  author = {R. Lenz and P. Meer and M. Hauta-Kasari},
  title = {Spectral-Based Illumination Estimation and Color Correction},
  booktitle = {Proc. 10th Scandinavian Conference on Image Analysis},
  year = {1997},
  pages = {885--892}
}
Lenz, R., Meer, P. and Hauta-Kasari, M. Spectral-Based Illumination Estimation and Color Image Normalization 1997
Vol. 2AIC Color 97, pp. 503-506 
inproceedings  
BibTeX:
@inproceedings{Lenz1997,
  author = {R. Lenz and P. Meer and M. Hauta-Kasari},
  title = {Spectral-Based Illumination Estimation and Color Image Normalization},
  booktitle = {AIC Color 97},
  publisher = {The Color Science Association of Japan},
  year = {1997},
  volume = {2},
  pages = {503--506}
}
Lenz, R. and Svanberg, J. Group Theoretical Transforms and Statistical Properties of Image Spaces 1997 Signal and Image Representation in Combined Spaces  incollection  
BibTeX:
@incollection{Lenz1997d,
  author = {R. Lenz and J. Svanberg},
  title = {Group Theoretical Transforms and Statistical Properties of Image Spaces},
  booktitle = {Signal and Image Representation in Combined Spaces},
  publisher = {Academic Press},
  year = {1997}
}
Assonov, M.V., Labunets, V.G., Lenz, R. and Labunets, E. Fast spectral algorithms for invariant pattern recognition and images matching based on modular invariants 1996
Vol. IIIProc. International Conference Image Processing, pp. 607-610 
inproceedings  
BibTeX:
@inproceedings{Assonov1996,
  author = {M. V. Assonov and V. G. Labunets and R. Lenz and E. Labunets},
  title = {Fast spectral algorithms for invariant pattern recognition and images matching based on modular invariants},
  booktitle = {Proc. International Conference Image Processing},
  year = {1996},
  volume = {III},
  pages = {607--610}
}
Hauta-Kasari, M., Parkkinen, J., Jaaskelainen, T. and Lenz, R. Generalized co-occurrence matrix for multispectral texture analysis 1996
Vol. vol.2Proceedings of the 13th International Conference on Pattern Recognition, pp. 785-9 
inproceedings  
Abstract: We present a new co-occurrence matrix based approach for multispectral texture analysis. The spectral and spatial domains of the multispectral textures are processed separately. The color space used in this study is represented by subspaces and it is classified by the averaged learning subspace method (ALSM). In the spatial domain we use a generalized co-occurrence matrix for vector valued pixels. The texture feature vectors are classified by the k-nearest neighbor (KNN) classifier and the multilayer perceptron (MLP) network. Experimental results of the multispectral texture segmentation are presented
BibTeX:
@inproceedings{Hauta-Kasari1996,
  author = {Hauta-Kasari, M. and Parkkinen, J. and Jaaskelainen, T. and Lenz, R.},
  title = {Generalized co-occurrence matrix for multispectral texture analysis},
  booktitle = {Proceedings of the 13th International Conference on Pattern Recognition},
  publisher = {IEEE Comput. Soc. Press},
  year = {1996},
  volume = {vol.2},
  pages = {785--9}
}
Lenz, R. and Homma, K. Rotational Symmetry: The Lie group SO(3) and its representations 1996
Vol. IIIProc. International Conference Image Processing, pp. 203-206 
inproceedings  
BibTeX:
@inproceedings{Lenz1996,
  author = {R. Lenz and K. Homma},
  title = {Rotational Symmetry: The Lie group SO(3) and its representations},
  booktitle = {Proc. International Conference Image Processing},
  year = {1996},
  volume = {III},
  pages = {203--206}
}
Lenz, R., Österberg, M., Hiltunen, J., Jaaskelainen, T. and Parkkinen, J. Unsupervised filtering of color spectra 1996 Journal of the Optical Society of America A (Optics, Image Science and Vision)
Vol. 13(7)J. Opt. Soc. Am. A, Opt. Image Sci. Vis. (USA), pp. 1315-24 
article  
Abstract: We describe a class of unsupervised systems that extract features from databases of reflectance spectra that sample color space in a way that reflects the properties of human color perception. The systems find the internal weight coefficients by optimizing an energy function. We describe several energy functions based on second- and fourth-order statistical moments of the computed output values. We also investigate the effects of imposing boundary conditions on the filter coefficients and the performance of the resulting systems for the databases with the reflectance spectra. The experiments show that the weight matrix for one of the systems is very similar to the eigenvector system, whereas the second type of system tries to rotate the eigenvector system in such a way that the resulting filters partition the spectrum into different bands. We also show how the system can be forced to use weight vectors with positive coefficients. Weight vectors are then approximated with Gaussian quadrature methods
BibTeX:
@article{Lenz1996a,
  author = {Lenz, R. and Österberg, M. and Hiltunen, J. and Jaaskelainen, T. and Parkkinen, J.},
  title = {Unsupervised filtering of color spectra},
  booktitle = {J. Opt. Soc. Am. A, Opt. Image Sci. Vis. (USA)},
  journal = {Journal of the Optical Society of America A (Optics, Image Science and Vision)},
  publisher = {Opt. Soc. America},
  year = {1996},
  volume = {13},
  number = {7},
  pages = {1315--24}
}
Lenz, R. Investigation of Receptive Fields using Representations of Dihedral Groups 1995 Journal of Visual Communication and Image Representation
Vol. 6(3), pp. 209-227 
article  
BibTeX:
@article{Lenz1995d,
  author = {R. Lenz},
  title = {Investigation of Receptive Fields using Representations of Dihedral Groups},
  journal = {Journal of Visual Communication and Image Representation},
  year = {1995},
  volume = {6},
  number = {3},
  pages = {209--227}
}
Lenz, R. and Österberg, M. Filtering: Invariance, Information Extraction and Learning 1995
Vol. 3Progress in Neural Networks, pp. 65-98 
inproceedings  
BibTeX:
@inproceedings{Lenz1995c,
  author = {Reiner Lenz and Mats Österberg},
  title = {Filtering: Invariance, Information Extraction and Learning},
  booktitle = {Progress in Neural Networks},
  publisher = {Ablex Publishing Corporation},
  year = {1995},
  volume = {3},
  pages = {65--98}
}
Lenz, R., Österberg, M., Hiltunen, J., Jaaskelainen, T. and Parkkinen, J. Exploring color spaces with unsupervised filters and Gaussian Quadrature 1995 Proc. Swedish Society for Automated Image Analysis, pp. 49-52  inproceedings  
BibTeX:
@inproceedings{Lenz1995,
  author = {Reiner Lenz and Mats Österberg and Jouni Hiltunen and Timo Jaaskelainen and Jussi Parkkinen},
  title = {Exploring color spaces with unsupervised filters and Gaussian Quadrature},
  booktitle = {Proc. Swedish Society for Automated Image Analysis},
  year = {1995},
  pages = {49--52}
}
Lenz, R., Österberg, M., Hiltunen, J., Jaaskelainen, T. and Parkkinen, J. Unsupervised Filtering of Color Spectra 1995 Proc. Scandinavian Conf. Image Analysis, pp. 803-810  inproceedings  
BibTeX:
@inproceedings{Lenz1995a,
  author = {Reiner Lenz and Mats Österberg and Jouni Hiltunen and Timo Jaaskelainen and Jussi Parkkinen},
  title = {Unsupervised Filtering of Color Spectra},
  booktitle = {Proc. Scandinavian Conf. Image Analysis},
  year = {1995},
  pages = {803--810}
}
Lenz, R. and Svanberg, J. Group Theoretical Transforms and Their Applications in Image Coding 1995 Proc. Int. Conf. Accoustics, Speech and Sig. Proc.  inproceedings  
BibTeX:
@inproceedings{Lenz1995b,
  author = {Reiner Lenz and Jonas Svanberg},
  title = {Group Theoretical Transforms and Their Applications in Image Coding},
  booktitle = {Proc. Int. Conf. Accoustics, Speech and Sig. Proc.},
  year = {1995}
}
Österberg, M. and Lenz, R. On parallel selective principal component analysis 1995 Proc. 1995 Swedish Conference on Connectionism, pp. 67-76  inproceedings  
BibTeX:
@inproceedings{Osterberg1995,
  author = {Mats Österberg and Reiner Lenz},
  title = {On parallel selective principal component analysis},
  booktitle = {Proc. 1995 Swedish Conference on Connectionism},
  publisher = {Lawrence Erlbaum Ass.},
  year = {1995},
  pages = {67--76}
}
Lenz, R. Group Theoretical Transforms in Image Processing 1994 Current Topics in Pattern Recognition Research,1, pp. 83-106  incollection  
BibTeX:
@incollection{Lenz1994,
  author = {Reiner Lenz},
  title = {Group Theoretical Transforms in Image Processing},
  booktitle = {Current Topics in Pattern Recognition Research,1},
  publisher = {Research Trends},
  year = {1994},
  pages = {83--106}
}
Lenz, R. and Meer, P. Experimental investigation of projection and permutation invariants 1994 Pattern Recognition Letters
Vol. 15(8), pp. 751-760 
article URL 
Abstract: The cross-ratio is the most popular projective invariant. It is invariant under projective transformation but it changes its value under permutation of the arguments. Using the cross-ratio it is however possible to construct invariants that are unchanged under both projections and permutations. There are three different types of these invariants: bounded rational functions, unbounded rational functions and absolute values of rational functions of the cross-ratio. All of them are equivalent under ideal, noise-free conditions. In this paper we investigate the properties of these functions under noise.
BibTeX:
@article{Lenz1994b,
  author = {Lenz, Reiner and Meer, Peter},
  title = {Experimental investigation of projection and permutation invariants},
  journal = {Pattern Recognition Letters},
  year = {1994},
  volume = {15},
  number = {8},
  pages = {751--760},
  url = {http://www.sciencedirect.com/science/article/B6V15-48M320M-92/2/71852426a9f2be72f81ffba05395f5a7}
}
Lenz, R. and Meer, P. Point configuration invariants under simultaneous projective and permutation transformations 1994 Pattern Recognition
Vol. 27(11), pp. 1523-1532 
article URL 
Abstract: The projective invariants used in computer vision today are permutation-sensitive since their value depends on the order in which the features were considered in the computation. We derive, using tools from representation theory, the projective and permutation (p2) invariants of the four collinear and the five coplanar points configurations. The p2-invariants are insensitive to both projective transformations and changes in the labeling of the points. When used as model database indexing functions in object recognition systems, the p2-invariants yield a significant speedup. Permutation invariants for affine transformations are also discussed.
BibTeX:
@article{Lenz1994c,
  author = {Lenz, Reiner and Meer, Peter},
  title = {Point configuration invariants under simultaneous projective and permutation transformations},
  journal = {Pattern Recognition},
  year = {1994},
  volume = {27},
  number = {11},
  pages = {1523--1532},
  url = {http://www.sciencedirect.com/science/article/B6V14-48MPN3T-19N/2/d0c495877762d52010646801a42dfffd}
}
Lenz, R. and Österberg, M. Neural Networks for Unsupervised Linear Feature Extraction 1994 Connectionism in a broad perspective, pp. 139-148  incollection  
BibTeX:
@incollection{Lenz1994a,
  author = {Reiner Lenz and Mats Österberg},
  title = {Neural Networks for Unsupervised Linear Feature Extraction},
  booktitle = {Connectionism in a broad perspective},
  publisher = {Ellis Horwood},
  year = {1994},
  pages = {139--148}
}
Meer, P., Ramakrishna, S. and Lenz, R. Correspondence of coplanar features through p2-invariant representations 1994
Vol. vol.1Proceedings of the 12th IAPR International Conference on Pattern Recognition (Cat. No.94CH3440-5), pp. 196-200 
inproceedings  
Abstract: The correspondence between two coplanar sets of points (or lines) is established making use of a novel invariant representation of five-tuples of features. The projective/permutation (p2) invariants are insensitive to the order of the features in the computation and thus provide a significant speedup in matching. Performance degradation due to the noise sensitivity of the invariants is avoided by using context independent constraints (noncollinearity of points, preservation of the convex hull); and by accumulating the feature correspondence hypotheses in a contingency table. Full projective correspondence can be recovered reliably for positional uncertainty of several pixels or in the presence of outliers
BibTeX:
@inproceedings{Meer1994a,
  author = {Meer, P. and Ramakrishna, S. and Lenz, R.},
  title = {Correspondence of coplanar features through p2-invariant representations},
  booktitle = {Proceedings of the 12th IAPR International Conference on Pattern Recognition (Cat. No.94CH3440-5)},
  publisher = {IEEE Comput. Soc. Press},
  year = {1994},
  volume = {vol.1},
  pages = {196--200}
}
Meer, P., Ramakrishna, S. and Lenz, R. Correspondence of coplanar features through P2-invariant representations 1994 Lecture Notes in Computer Science
Vol. 825LNCS-825, pp. 473-492 
inproceedings URL 
BibTeX:
@inproceedings{Meer1994,
  author = {Meer, Peter and Ramakrishna, Sudhir and Lenz, Reiner},
  title = {Correspondence of coplanar features through P2-invariant representations},
  booktitle = {LNCS-825},
  journal = {Lecture Notes in Computer Science},
  year = {1994},
  volume = {825},
  pages = {473--492},
  url = {http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/3-540-58240-1_25}
}
Österberg, M. Quality Functions for Parallel Selective Principal Component Analysis 1994 School: Linköping University  phdthesis  
BibTeX:
@phdthesis{Osterberg1994a,
  author = {M. Österberg},
  title = {Quality Functions for Parallel Selective Principal Component Analysis},
  school = {Linköping University},
  year = {1994}
}
Österberg, M. and Lenz, R. Unsupervised Parallel Feature Extraction from First Principles 1994 Advances in Neural Information Processing Systems 6, pp. 136-144  inproceedings  
BibTeX:
@inproceedings{Osterberg1994,
  author = {M. Österberg and R. Lenz},
  title = {Unsupervised Parallel Feature Extraction from First Principles},
  booktitle = {Advances in Neural Information Processing Systems 6},
  publisher = {Morgan, Kaufmann},
  year = {1994},
  pages = {136--144}
}
Lenz, R. On P^2 Invariance 1993 Proc. of the Swedish Society for Automated Image Analysis Symposium, Gothenburg, Sweden  inproceedings  
BibTeX:
@inproceedings{Lenz1993b,
  author = {Reiner Lenz},
  title = {On P^2 Invariance},
  booktitle = {Proc. of the Swedish Society for Automated Image Analysis Symposium, Gothenburg, Sweden},
  year = {1993}
}
Lenz, R. Using Representations of the Dihedral Groups in the Design of Early Vision Filters 1993
Vol. VProc. Int. Conf. Accoustics, Speech and Sig. Proc., pp. 165-168 
inproceedings  
BibTeX:
@inproceedings{Lenz1993c,
  author = {Reiner Lenz},
  title = {Using Representations of the Dihedral Groups in the Design of Early Vision Filters},
  booktitle = {Proc. Int. Conf. Accoustics, Speech and Sig. Proc.},
  year = {1993},
  volume = {V},
  pages = {165--168}
}
Lenz, R. and Meer, P. Projection and Permutation Invariant Object Recognition 1993 Proc. of the 8th Scandinavian Conference on Image Analysis, pp. 389-396  inproceedings  
BibTeX:
@inproceedings{Lenz1993,
  author = {Reiner Lenz and Peter Meer},
  title = {Projection and Permutation Invariant Object Recognition},
  booktitle = {Proc. of the 8th Scandinavian Conference on Image Analysis},
  publisher = {NOBIM},
  year = {1993},
  pages = {389--396}
}
Meer, P., Ramakrishna, S. and Lenz, R. Indexing power of the projective/permutation invariant of five coplanar points 1993 Applications of Invariance in Computer Vision II, pp. 133-150  inproceedings  
BibTeX:
@inproceedings{Meer1993,
  author = {Peter Meer and Sudhir Ramakrishna and Reiner Lenz},
  title = {Indexing power of the projective/permutation invariant of five coplanar points},
  booktitle = {Applications of Invariance in Computer Vision II},
  year = {1993},
  pages = {133--150},
  note = {Ponta-Delgada, Azores, 9-14 Oct. 1993}
}
Seger, O. Model building and restoration with applications in confocal microscopy 1993 School: Linköping University  phdthesis  
BibTeX:
@phdthesis{Seger1993,
  author = {O. Seger},
  title = {Model building and restoration with applications in confocal microscopy},
  school = {Linköping University},
  year = {1993}
}
Lenz, R. Group Theoretical Feature Extraction: Weighted Invariance and Texture Analysis 1992 Selected Papers from the 7th Scandinavian Conference on Image Analysis, pp. 63-70  incollection  
BibTeX:
@incollection{Lenz1992c,
  author = {Reiner Lenz},
  title = {Group Theoretical Feature Extraction: Weighted Invariance and Texture Analysis},
  booktitle = {Selected Papers from the 7th Scandinavian Conference on Image Analysis},
  publisher = {World Scientific},
  year = {1992},
  pages = {63--70}
}
Lenz, R. and Österberg, M. A Method for unsupervised linear feature extraction using fourth order moments 1992 Proc. Swedish Society for Automated Image Analysis Symposium, Uppsala, Sweden  inproceedings  
BibTeX:
@inproceedings{Lenz1992a,
  author = {Reiner Lenz and Mats Österberg},
  title = {A Method for unsupervised linear feature extraction using fourth order moments},
  booktitle = {Proc. Swedish Society for Automated Image Analysis Symposium, Uppsala, Sweden},
  year = {1992}
}
Lenz, R. and Österberg, M. A new method for unsupervised linear feature extraction, using fourth order moments 1992 Proceedings. 11th IAPR International Conference on Pattern Recognition. Vol.II. Conference B: Pattern Recognition Methodology and Systems, pp. 71-4  inproceedings  
Abstract: The authors discuss two classes of unsupervised feature extraction methods. They show that a system based on second order moments can learn the Karhunen-Loeve expansion in parallel. Then they show that systems based on second order moments only have important drawbacks. The second class of systems described avoids this problem by using fourth order moments. Since these systems are much harder to analyze the authors demonstrate some of their advantages with the help of some experiments
BibTeX:
@inproceedings{Lenz1992f,
  author = {Lenz, R. and Österberg, M.},
  title = {A new method for unsupervised linear feature extraction, using fourth order moments},
  booktitle = {Proceedings. 11th IAPR International Conference on Pattern Recognition. Vol.II. Conference B: Pattern Recognition Methodology and Systems},
  publisher = {IEEE Comput. Soc. Press},
  year = {1992},
  pages = {71--4}
}
Lenz, R. and Österberg, M. Computing the Karhunen-Loéve expansion with a parallel, unsupervised filter system 1992 Neural Computation
Vol. 4, pp. 382-392 
article  
BibTeX:
@article{Lenz1992d,
  author = {R. Lenz and M. Österberg},
  title = {Computing the Karhunen-Loéve expansion with a parallel, unsupervised filter system},
  journal = {Neural Computation},
  year = {1992},
  volume = {4},
  pages = {382--392}
}
Lenz, R. and Seger, O. Group Theoretical Methods in 3-D Image Processing 1992 Leading Edge of Super Light Microscopy, Tokyo, 1992  inproceedings  
BibTeX:
@inproceedings{Lenz1992,
  author = {Reiner Lenz and Olle Seger},
  title = {Group Theoretical Methods in 3-D Image Processing},
  booktitle = {Leading Edge of Super Light Microscopy, Tokyo, 1992},
  year = {1992}
}
Lenz, R. and Seger, O. Group Theoretical Methods in Image Science 1992 New Trends on Scanning Optical Microscopy, OITDA Workshop, Naha, Japan, 1992, pp. 161-166  inproceedings  
BibTeX:
@inproceedings{Lenz1992b,
  author = {Reiner Lenz and Olle Seger},
  title = {Group Theoretical Methods in Image Science},
  booktitle = {New Trends on Scanning Optical Microscopy, OITDA Workshop, Naha, Japan, 1992},
  year = {1992},
  pages = {161--166}
}
Lenz Reiner anÖsterberg, M. A new method for unsupervised linear feature extraction, using fourth-order moments 1992 Pattern Recognition Letters
Vol. 13(12), pp. 827-836 
article URL 
Abstract: In this paper we investigate an unsupervised linear feature extraction system based on the second- and fourth-order moments of the input covariance function. First we demonstrate some drawbacks of systems based on second-order moments (including all Karhunen-Loeve systems). Then we introduce a new version of our Learning filter system that is based on fourth-order moments. We show that this system has the same modular structure as our previous (second-order) systems. Then we discuss some advantages of this new system with the help of some examples. In the first example we demonstrate that this new system can detect meaningful structures even in those subspaces that belong to the same eigenvalue of the covariance matrix. Systems based on second-order moments are unable to find such structures. In the second example we train the system with two pattern sequences that have exactly the same second-order moments. We show that the system stabilizes indeed in two different states that reflect relevant properties of the whole trainings sequence. In the last example we demonstrate that the feature vectors produced by the new system are better adapted to a special type nonlinear post-processing that is motivated by the group-theoretically based filter design methodology.
BibTeX:
@article{Lenz1992e,
  author = {Lenz, Reiner anÖsterberg, Mats},
  title = {A new method for unsupervised linear feature extraction, using fourth-order moments},
  journal = {Pattern Recognition Letters},
  year = {1992},
  volume = {13},
  number = {12},
  pages = {827--836},
  url = {http://www.sciencedirect.com/science/article/B6V15-48N55FK-2P/2/81aeea5074139a17b1b82e290ed3563f}
}
Seger, O. and Lenz, R. Anisotropic Image Restoration 1992 Proc. Swedish Society for Automated Image Analysis Symposium, Uppsala, Sweden  inproceedings  
BibTeX:
@inproceedings{Seger1992,
  author = {Olle Seger and Reiner Lenz},
  title = {Anisotropic Image Restoration},
  booktitle = {Proc. Swedish Society for Automated Image Analysis Symposium, Uppsala, Sweden},
  year = {1992}
}
Seger, O. and Lenz, R. Experiments with on operator model of a confocal microscope 1992 Proc of SPIE conference on Biomedical Image Processing III and 3-D Microscopy, San Jose, USA  inproceedings  
BibTeX:
@inproceedings{Seger1992a,
  author = {Olle Seger and Reiner Lenz},
  title = {Experiments with on operator model of a confocal microscope},
  booktitle = {Proc of SPIE conference on Biomedical Image Processing III and 3-D Microscopy, San Jose, USA},
  year = {1992}
}
Seger, O. and Lenz, R. Modeling of the point spread function of laser scanning microscopes using canonical transforms 1992 Journal of Visual Communication and Image Representation
Vol. 3(4), pp. 364-380 
article  
BibTeX:
@article{Seger1992b,
  author = {Olle Seger and R. Lenz},
  title = {Modeling of the point spread function of laser scanning microscopes using canonical transforms},
  journal = {Journal of Visual Communication and Image Representation},
  year = {1992},
  volume = {3},
  number = {4},
  pages = {364--380}
}
Lenz, R. Group Theoretical Feature Extraction: Weighted Invariance and Texture Analysis 1991 Proc. Swedish Society for Automated Image Analysis Symposium, Stockholm, Sweden  inproceedings  
BibTeX:
@inproceedings{Lenz1991a,
  author = {Reiner Lenz},
  title = {Group Theoretical Feature Extraction: Weighted Invariance and Texture Analysis},
  booktitle = {Proc. Swedish Society for Automated Image Analysis Symposium, Stockholm, Sweden},
  year = {1991}
}
Lenz, R. Group Theoretical Feature Extraction: Weighted Invariance and Texture Analysis 1991 7th Scandinavian Conference on Image Analysis  inproceedings  
BibTeX:
@inproceedings{Lenz1991b,
  author = {Reiner Lenz},
  title = {Group Theoretical Feature Extraction: Weighted Invariance and Texture Analysis},
  booktitle = {7th Scandinavian Conference on Image Analysis},
  year = {1991}
}
Lenz, R. On probabilistic invariance 1991 Neural Networks
Vol. 4(5), pp. 627-641 
article URL 
Abstract: The invariance principle is one important design principle in low-level pattern recognition. In the first part of this paper we investigate some theoretical aspects of this principle. In the second part we show how an adaptive filter system reacts to pattern sets that involve some kind of invariance.In its most general, group-theoretical form the invariance principle can be formulated as follows:We assume that we have a class of patterns of interest pi : i [epsilon] I and a given pattern q. The problem is to decide if q was a pattern of interest or not, i.e., if q = pi0 for some i0 [epsilon] I. If the patterns pi are generated from a common prototype pattern p0 with the help of transformations gi and if these transformations gi form a group G then this problem can be solved by finding maximum correlation filter sets. The relation between these filter sets and the prototype pattern p0 and the transformation group G is completely known.The construction of the filter functions is, however, based on the assumption that all transformations gi [epsilon] G (and therefore also all patterns pi) appear equally often. The purpose of this paper is the generalization of the filter construction process to pattern classes whose elements obey some probability distribution. In the special cases of 2-D rotation invariance and scale invariance, we will show how the maximum correlation filters depend on the prototype pattern, the transformation group, and the probability distribution. We will also sketch the theory for the case of arbitrary compact transformation groups and what type of problems turn up in this case.In the last part of the paper we describe an adaptive filter system that can find the maximum correlation filter functions automatically from a given set of patterns of interest. This filter system also uses a kind of maximum separation principle so that the resulting feature vectors can be easily used by classifiers. We demonstrate how such a filter system stabilizes in states that correspond to the theoretically derived filter functions and how this filter system reacts to invariance properties in the trainings set.
BibTeX:
@article{Lenz1991d,
  author = {Lenz, Reiner},
  title = {On probabilistic invariance},
  journal = {Neural Networks},
  year = {1991},
  volume = {4},
  number = {5},
  pages = {627--641},
  url = {http://www.sciencedirect.com/science/article/B6T08-485RHJV-29/2/db2d62a1a9b6015b0f9ff469350c8552}
}
Lenz, R. and Österberg, M. A parallel learning filter system that learns the KL-expansion from examples 1991 Proc. First IEEE-SP Workshop on Neural Networks for Signal Processing (Sept. 91)  inproceedings  
BibTeX:
@inproceedings{Lenz1991,
  author = {Reiner Lenz and Mats Österberg},
  title = {A parallel learning filter system that learns the KL-expansion from examples},
  booktitle = {Proc. First IEEE-SP Workshop on Neural Networks for Signal Processing (Sept. 91)},
  year = {1991}
}
Lenz, R. and Österberg, M. Learning filter systems with maximum correlation and maximum separation properties 1991
Vol. 1469Proc. SPIE - Int. Soc. Opt. Eng. (USA), pp. 784-95 
inproceedings  
Abstract: Describe a system that can be used as a feature extraction unit in a low-level pattern recognition system. The authors assume that such a system acts as a linear mapping between the pattern space and the feature space. It can therefore be completely described by a number of filter kernels. These filter kernels are usually constructed by the designer of the system. In the approach to filter design described in the paper the authors do not create the filter kernels manually. Instead they feed the system during the trainings period with a representative selection of the patterns that they want to recognize. During the trainings phase they use a learning rule (based on a quality function) to update the current form of the filter functions
BibTeX:
@inproceedings{Lenz1991c,
  author = {Lenz, R. and Österberg, M.},
  title = {Learning filter systems with maximum correlation and maximum separation properties},
  booktitle = {Proc. SPIE - Int. Soc. Opt. Eng. (USA)},
  year = {1991},
  volume = {1469},
  pages = {784--95}
}
Magnusson, M., Lenz, R. and Danielsson, P.-E. Evaluation of methods for shaded surface display of CT-volumes 1991 Computerized Medical Imaging and Graphics
Vol. 15(4), pp. 247-256 
article  
BibTeX:
@article{Magnusson1991,
  author = {Maria Magnusson and Reiner Lenz and Per-Erik Danielsson},
  title = {Evaluation of methods for shaded surface display of CT-volumes},
  journal = {Computerized Medical Imaging and Graphics},
  year = {1991},
  volume = {15},
  number = {4},
  pages = {247--256}
}
Österberg, M. and Lenz, R. Learning Filter Systems: Basic principles and some applications 1991 7th Scandinavian Conference on Image Analysis  inproceedings  
BibTeX:
@inproceedings{Osterberg1991a,
  author = {Mats Österberg and Reiner Lenz},
  title = {Learning Filter Systems: Basic principles and some applications},
  booktitle = {7th Scandinavian Conference on Image Analysis},
  year = {1991}
}
Österberg, M. and Lenz, R. Learning Filter Systems: Recent Developments and New Experiments 1991 Proc. Swedish Society for Automated Image Analysis Symposium, Stockholm, Sweden  inproceedings  
BibTeX:
@inproceedings{Osterberg1991,
  author = {Mats Österberg and Reiner Lenz},
  title = {Learning Filter Systems: Recent Developments and New Experiments},
  booktitle = {Proc. Swedish Society for Automated Image Analysis Symposium, Stockholm, Sweden},
  year = {1991}
}
Seger, O. and Lenz, R. Modelling a confocal microscope with operator methods 1991 Proc. Swedish Society for Automated Image Analysis Symposium, Stockholm, Sweden  inproceedings  
BibTeX:
@inproceedings{Seger1991,
  author = {Olle Seger and Reiner Lenz},
  title = {Modelling a confocal microscope with operator methods},
  booktitle = {Proc. Swedish Society for Automated Image Analysis Symposium, Stockholm, Sweden},
  year = {1991}
}
Lenz, R. A Group Theoretical Investigation of Motion 1990 Proc. Swedish Society for Automated Image Analysis Symposium, Linköping, Sweden  inproceedings  
BibTeX:
@inproceedings{Lenz1990,
  author = {Reiner Lenz},
  title = {A Group Theoretical Investigation of Motion},
  booktitle = {Proc. Swedish Society for Automated Image Analysis Symposium, Linköping, Sweden},
  year = {1990}
}
Lenz, R. Group invariant pattern recognition 1990 Pattern Recognition
Vol. 23(1-2), pp. 199-217 
article URL 
Abstract: In this paper we develop a group theoretical model for the feature extraction part of pattern recognition systems. We argue that the features used should reflect the regularities in the environment in which the system exists. We develop first a group theoretical model to describe these regularities, and then we show how to construct a feature extraction system that reflects these regularities. We show why the so found filter functions often appear as solutions to optimality problems and why they often have some nice properties such as invariance under Fourier transformation. We will mainly investigate problems connected to the group of rotations (in 2-D and 3-D space) but we will touch other types of symmetries as well.
BibTeX:
@article{Lenz1990f,
  author = {Lenz, Reiner},
  title = {Group invariant pattern recognition},
  journal = {Pattern Recognition},
  year = {1990},
  volume = {23},
  number = {1-2},
  pages = {199--217},
  url = {http://www.sciencedirect.com/science/article/B6V14-48MPJMT-K2/2/845c1457606b0f7db207150898da031e}
}
Lenz, R. Group Theoretical Methods in Image Processing 1990   book  
BibTeX:
@book{Lenz1990e,
  author = {R. Lenz},
  title = {Group Theoretical Methods in Image Processing},
  publisher = {Springer Verlag},
  year = {1990}
}
Lenz, R. and Österberg, M. Learning Filter Systems 1990 Proc. Swedish Society for Automated Image Analysis Symposium, Linköping, Sweden  inproceedings  
BibTeX:
@inproceedings{Lenz1990a,
  author = {Reiner Lenz and Mats Österberg},
  title = {Learning Filter Systems},
  booktitle = {Proc. Swedish Society for Automated Image Analysis Symposium, Linköping, Sweden},
  year = {1990}
}
Lenz, R. and Österberg, M. Learning Filter Systems 1990 Proc. Int. Neural Networks Conference, Paris  inproceedings  
BibTeX:
@inproceedings{Lenz1990b,
  author = {Reiner Lenz and Mats Österberg},
  title = {Learning Filter Systems},
  booktitle = {Proc. Int. Neural Networks Conference, Paris},
  year = {1990}
}
Lenz, R. and Österberg, M. Learning Filter Systems 1990 Proc. Int. Joint Conference on Neural Networks, San Diego  inproceedings  
BibTeX:
@inproceedings{Lenz1990d,
  author = {Reiner Lenz and Mats Österberg},
  title = {Learning Filter Systems},
  booktitle = {Proc. Int. Joint Conference on Neural Networks, San Diego},
  year = {1990}
}
Lenz, R. and Seger, O. A review of operator methods in Fourier optics 1990 Proc. Micro 90; Transactions of the Royal Microscopical Society, pp. 243-246  inproceedings  
BibTeX:
@inproceedings{Lenz1990c,
  author = {Reiner Lenz and Olle Seger},
  title = {A review of operator methods in Fourier optics},
  booktitle = {Proc. Micro 90; Transactions of the Royal Microscopical Society},
  publisher = {A. Hilger},
  year = {1990},
  pages = {243--246}
}
Grönqvist, A. and Lenz, R. Detection of Blood Vessels in 3-D MR-Images 1989 Proc. of the Swedish Society for Automated Image Analysis Symposium, Gothenburg, Sweden  inproceedings  
BibTeX:
@inproceedings{Gronqvist1989,
  author = {Anders Grönqvist and Reiner Lenz},
  title = {Detection of Blood Vessels in 3-D MR-Images},
  booktitle = {Proc. of the Swedish Society for Automated Image Analysis Symposium, Gothenburg, Sweden},
  year = {1989}
}
Grönqvist, A. and Lenz, R. Detection of Blood Vessels in 3-D MR-Images 1989 Proc. of the 1989 IEEE/INNS International Joint Conference on Neural Nets  inproceedings  
BibTeX:
@inproceedings{Gronqvist1989a,
  author = {Anders Grönqvist and Reiner Lenz},
  title = {Detection of Blood Vessels in 3-D MR-Images},
  booktitle = {Proc. of the 1989 IEEE/INNS International Joint Conference on Neural Nets},
  year = {1989}
}
Lenz, R. A Group Theoretical Approach to Filter Design 1989 Proc. Int. Conf. Accoustics, Speech and Sig. Proc.  inproceedings  
BibTeX:
@inproceedings{Lenz1989a,
  author = {Reiner Lenz},
  title = {A Group Theoretical Approach to Filter Design},
  booktitle = {Proc. Int. Conf. Accoustics, Speech and Sig. Proc.},
  year = {1989}
}
Lenz, R. Describing and recognizing group-invariant pattern classes with group-sampling 1989 Pattern Recognition Letters
Vol. 9(3), pp. 169-173 
article URL 
Abstract: In this paper we investigate how a pattern recognition system can describe a whole class of patterns and how it can extract these patterns from an unknown image. We assume that the pattern class is defined in terms of a group operation and a prototype pattern. We will then construct a class of symbols that describe such a class uniquely. Finally we discuss the problem how to decide if a given, unknown gray value pattern was a member of a given pattern class or not. We will mainly discuss the problem in the case where the group defining the pattern class is a rotation group (in two or three dimensions) but we will mention results for other interesting groups as well.
BibTeX:
@article{Lenz1989b,
  author = {Lenz, Reiner},
  title = {Describing and recognizing group-invariant pattern classes with group-sampling},
  journal = {Pattern Recognition Letters},
  year = {1989},
  volume = {9},
  number = {3},
  pages = {169--173},
  url = {http://www.sciencedirect.com/science/article/B6V15-48MXRX6-8V/2/4bf44b2cefa566b16b3f8c6d1b1bc210}
}
Lenz, R. Group-theoretical model of feature extraction 1989 Journal of the Optical Society of America A (Optics and Image Science)
Vol. 6(6)J. Opt. Soc. Am. A, Opt. Image Sci. (USA), pp. 827-34 
article  
Abstract: A group-theoretically motivated investigation of feature extraction is described. A feature extraction unit is defined as a complex-valued function on a signal space. It is assumed that the signal space possesses a group-theoretically defined regularity that the authors introduce. First the concept of a symmetrical signal space is derived. Feature mappings then are introduced on signal spaces and some properties of feature mappings on symmetrical signal spaces are investigated. Next the investigation is restricted to linear features, and an overview of all possible linear features is given. Also it is shown how a set of linear features can be used to construct a nonlinear feature that has the same value for all patterns in a class of similar patterns. These results are used to construct filter functions that can be used to detect patterns in two- and three-dimensional images independent of the orientation of the pattern in the image. Finally it is sketched briefly how the theory developed here can be applied to solve other, symmetrical problems in imaging processing
BibTeX:
@article{Lenz1989c,
  author = {Lenz, R.},
  title = {Group-theoretical model of feature extraction},
  booktitle = {J. Opt. Soc. Am. A, Opt. Image Sci. (USA)},
  journal = {Journal of the Optical Society of America A (Optics and Image Science)},
  year = {1989},
  volume = {6},
  number = {6},
  pages = {827--34}
}
Lenz, R. and Österberg, M. Adaptive, Invariant Filter Systems 1989 Proc. of the Swedish Society for Automated Image Analysis Symposium, Gothenburg, Sweden  inproceedings  
BibTeX:
@inproceedings{Lenz1989,
  author = {Reiner Lenz and Mats Österberg},
  title = {Adaptive, Invariant Filter Systems},
  booktitle = {Proc. of the Swedish Society for Automated Image Analysis Symposium, Gothenburg, Sweden},
  year = {1989}
}
Lenz, R. A group theoretical approach to filter design 1988 Proc. of the Swedish Society for Automated Image Analysis Symposium, Lund, Sweden  inproceedings  
BibTeX:
@inproceedings{Lenz1988,
  author = {Reiner Lenz},
  title = {A group theoretical approach to filter design},
  booktitle = {Proc. of the Swedish Society for Automated Image Analysis Symposium, Lund, Sweden},
  year = {1988}
}
Magnusson, M., Lenz, R. and Danielsson, P.-E. A comparison of some shaded surface display methods 1988 Proc. of the Swedish Society for Automated Image Analysis Symposium, Lund, Sweden  inproceedings  
BibTeX:
@inproceedings{Magnusson1988,
  author = {Maria Magnusson and Reiner Lenz and Per-Erik Danielsson},
  title = {A comparison of some shaded surface display methods},
  booktitle = {Proc. of the Swedish Society for Automated Image Analysis Symposium, Lund, Sweden},
  year = {1988}
}
Magnusson, M., Lenz, R. and Danielsson, P.-E. Evaluation of methods for shaded surface display of CT-volumes 1988 9th International Conference on Pattern Recognition (IEEE Cat. No.88CH2614-6), pp. 1287-94  inproceedings  
Abstract: Twelve methods are evaluated to analyze an ideal sphere and a real human skull. They are different combinations of principles for detection of the surface to be displayed (gray-value threshold, gradient threshold, and zero-crossing of the second derivative), localizing this surface in space (including both grid-point accuracy and subvoxel accuracy), and finally estimating the direction of the surface normal (from the gradient in the 2-D depth image and from the gradient in the 3-D volume). The best quality is obtained by zero-crossing detection, subvoxel localization, and 3-D gradient orientation
BibTeX:
@inproceedings{Magnusson1988a,
  author = {Magnusson, M. and Lenz, R. and Danielsson, P.-E.},
  title = {Evaluation of methods for shaded surface display of CT-volumes},
  booktitle = {9th International Conference on Pattern Recognition (IEEE Cat. No.88CH2614-6)},
  publisher = {IEEE Comput. Soc. Press},
  year = {1988},
  pages = {1287--94}
}
Lenz, R. Optimal filters for the detection of linear patterns in 2-D and higher dimensional images 1987 Pattern Recognition
Vol. 20(2), pp. 163-172 
article URL 
Abstract: It is shown that the rotation-invariant operators form a set of orthogonal basis functions which is optimal for a wide range of 2-D and 3-D feature-detection operations. The optimality criterion used is based on the Karhunen-Loeve expansion of the local image data. This is a generalization of the work of Zucker and Hummel who showed that these filters are optimal filters for the detection of step edges in 2-D and 3-D images.
BibTeX:
@article{Lenz1987a,
  author = {Lenz, Reiner},
  title = {Optimal filters for the detection of linear patterns in 2-D and higher dimensional images},
  journal = {Pattern Recognition},
  year = {1987},
  volume = {20},
  number = {2},
  pages = {163--172},
  url = {http://www.sciencedirect.com/science/article/B6V14-48MPKNV-V5/2/7956336f8b2d6cc19d25bd79b0f03ee5}
}
Lenz, R. Rotation-invariant operators and scale-space filtering 1987 Pattern Recognition Letters
Vol. 6(3), pp. 151-154 
article URL 
Abstract: We analyse the `Laplacian of the Gaussian' approach with the help of rotation-invariant operators and we show how the original image is related to the Gaussian (and Laplace-) filtered version of it.
BibTeX:
@article{Lenz1987b,
  author = {Lenz, Reiner},
  title = {Rotation-invariant operators and scale-space filtering},
  journal = {Pattern Recognition Letters},
  year = {1987},
  volume = {6},
  number = {3},
  pages = {151--154},
  url = {http://www.sciencedirect.com/science/article/B6V15-48MXRGH-45/2/01c68de7cf9516ba6403b93dcca787c0}
}
Lenz, R. and Gudmundsson, B. 3-D Image Processing and Display - A Survey 1987 ACTA Stereologica
Vol. 6, Suppl. I, pp. 137-142 
article  
BibTeX:
@article{Lenz1987,
  author = {R. Lenz and Björn Gudmundsson},
  title = {3-D Image Processing and Display - A Survey},
  journal = {ACTA Stereologica},
  year = {1987},
  volume = {6, Suppl. I},
  pages = {137--142}
}
Lenz, R. 3-D Reconstruction with a Projection onto Convex Sets Algorithm 1986 Optics Communications
Vol. 57(1), pp. 21-25 
article  
BibTeX:
@article{Lenz1986b,
  author = {R. Lenz},
  title = {3-D Reconstruction with a Projection onto Convex Sets Algorithm},
  journal = {Optics Communications},
  year = {1986},
  volume = {57},
  number = {1},
  pages = {21--25}
}
Lenz, R. 3-D reconstruction with a projection onto convex sets algorithm 1986 Optics Communications
Vol. 57(1)Opt. Commun. (Netherlands), pp. 21-5 
article  
Abstract: A reconstruction scheme based on linear systems theory is described which improves the resolution of 3-D light microscopic images along the optical axis. The method iteratively eliminates the contributions from the out-of-focus planes. It converges to the true solution in the absence of noise
BibTeX:
@article{Lenz1986e,
  author = {Lenz, R.},
  title = {3-D reconstruction with a projection onto convex sets algorithm},
  booktitle = {Opt. Commun. (Netherlands)},
  journal = {Optics Communications},
  year = {1986},
  volume = {57},
  number = {1},
  pages = {21--5}
}
Lenz, R. Experiments in 3-D Image Processing 1986 Proc. of the Swedish Society for Automated Image Analysis Symposium, Uppsala, Sweden  inproceedings  
BibTeX:
@inproceedings{Lenz1986a,
  author = {Reiner Lenz},
  title = {Experiments in 3-D Image Processing},
  booktitle = {Proc. of the Swedish Society for Automated Image Analysis Symposium, Uppsala, Sweden},
  year = {1986}
}
Lenz, R. Reconstruction, Processing and Display of 3D-Images 1986 School: Linköping University, Sweden  phdthesis  
BibTeX:
@phdthesis{Lenz1986,
  author = {Reiner Lenz},
  title = {Reconstruction, Processing and Display of 3D-Images},
  school = {Linköping University, Sweden},
  year = {1986}
}
Lenz, R. Rotation-invariant operators 1986 Eighth International Conference on Pattern Recognition. Proceedings (Cat. No.86CH2342-4), pp. 1130-2  inproceedings  
Abstract: Rotation-invariant operators are described that are filters of the form f(x,y)=f(r,φ)=hn(r)exp(inφ) in the two dimensional case and f(X)=f(rU)=hn(r)Sn(U) in the higher-dimensional cases. Their usefulness is demonstrated for a large number of pattern recognition purposes, including edge and line detection. Some properties of these filters that make them a natural choice for the class of problems considered are summarized. It is shown how the weight functions hn can be constructed to make the resulting filters optimal in a certain sense. Some other applications where this type of function is useful are mentioned
BibTeX:
@inproceedings{Lenz1986g,
  author = {Lenz, R.},
  title = {Rotation-invariant operators},
  booktitle = {Eighth International Conference on Pattern Recognition. Proceedings (Cat. No.86CH2342-4)},
  publisher = {IEEE Comput. Soc. Press},
  year = {1986},
  pages = {1130--2}
}
Lenz, R. Rotation-invariant operators for 2D and higher dimensional images 1986 Advances in Image Processing and Pattern Recognition. Proceedings of the International Conference, pp. 164-8  inproceedings  
Abstract: The idea of detecting edges in digital images by fitting a surface to a neighborhood of each image point, introduced by Prewitt (1979), was modified by Hummel (1979), who selected the type of surfaces depending on the type of the interesting target patterns. His method thus consists of two steps: selecting the class of surfaces such that they fit the target patterns best in a mean square sense, and finding the surface in the selected class which approximates the image data best and deciding whether this surface fits the image data well enough. Results obtained are generalized in several ways. First it is proven that the rotation-invariant operators are optimal basis functions for a large class of features and it is shown how the weight function h(r) can be computed from the given features of interest. Secondly, the results are generalized to images of arbitrary dimension (two or more)
BibTeX:
@inproceedings{Lenz1986f,
  author = {Lenz, R.},
  title = {Rotation-invariant operators for 2D and higher dimensional images},
  booktitle = {Advances in Image Processing and Pattern Recognition. Proceedings of the International Conference},
  publisher = {North-Holland},
  year = {1986},
  pages = {164--8}
}
Lenz, R., Gudmundsson, B. and Lindskog, B. Manipulation and display of 3-D images for surgical planning 1986
Vol. 593Proc. SPIE - Int. Soc. Opt. Eng. (USA), pp. 96-102 
inproceedings  
Abstract: The authors describe some experiments in the processing and display of 3-D images from CT-scanners. In the first part they describe the implemented surface displays and in the second part they discuss some applications of 3-D image transformations
BibTeX:
@inproceedings{Lenz1986d,
  author = {Lenz, R. and Gudmundsson, B. and Lindskog, B.},
  title = {Manipulation and display of 3-D images for surgical planning},
  booktitle = {Proc. SPIE - Int. Soc. Opt. Eng. (USA)},
  year = {1986},
  volume = {593},
  pages = {96--102}
}
Lenz, R., Gudmundsson, B., Lindskog, B. and Danielsson, P.E. Display of Density Volumes 1986 IEEE Computer Graphics and Applications
Vol. 6(7), pp. 20-29 
article  
BibTeX:
@article{Lenz1986c,
  author = {R. Lenz and B. Gudmundsson and B. Lindskog and P. E. Danielsson},
  title = {Display of Density Volumes},
  journal = {IEEE Computer Graphics and Applications},
  year = {1986},
  volume = {6},
  number = {7},
  pages = {20--29}
}
Carlsson, K., Liljeborg, A., Majlöf, L., N.Åslund, Danielsson, P.E. and Lenz, R. Three-dimensional Microscopy using a Confocal Laser Scanning Microscope 1985 Optics Letters
Vol. 10, pp. 53-55 
article  
BibTeX:
@article{Carlsson1985,
  author = {K. Carlsson and A. Liljeborg and L. Majlöf and N.Åslund and P. E. Danielsson and R. Lenz},
  title = {Three-dimensional Microscopy using a Confocal Laser Scanning Microscope},
  journal = {Optics Letters},
  year = {1985},
  volume = {10},
  pages = {53--55}
}
Lenz, R. 3-D Filters for Noise Reduction and 3-D Display 1985 Proc. of the Swedish Society for Automated Image Analysis Symposium, Stockholm, Sweden  inproceedings  
BibTeX:
@inproceedings{Lenz1985,
  author = {Reiner Lenz},
  title = {3-D Filters for Noise Reduction and 3-D Display},
  booktitle = {Proc. of the Swedish Society for Automated Image Analysis Symposium, Stockholm, Sweden},
  year = {1985}
}
Lenz, R., Danielsson, P.-E. and Cronström, S. Application of 3-D Thinning and Filtering in the Display of 3-D Images 1985 Proc. of the 4th Scandinavian Conference on Image Analysis, Trondheim, Norway  inproceedings  
BibTeX:
@inproceedings{Lenz1985a,
  author = {Reiner Lenz and Per-Erik Danielsson and Staffan Cronström},
  title = {Application of 3-D Thinning and Filtering in the Display of 3-D Images},
  booktitle = {Proc. of the 4th Scandinavian Conference on Image Analysis, Trondheim, Norway},
  year = {1985}
}
Lenz, R., Danielsson, P.-E., Gudmundsson, B. and Edholm, P. Experiments in Processing and Display of 3D Radiography Images 1985 Proc. XIV ICMBE and VII ICMP, Espoo, Finland  inproceedings  
BibTeX:
@inproceedings{Lenz1985b,
  author = {Reiner Lenz and Per-Erik Danielsson and Björn Gudmundsson and Paul Edholm},
  title = {Experiments in Processing and Display of 3D Radiography Images},
  booktitle = {Proc. XIV ICMBE and VII ICMP, Espoo, Finland},
  year = {1985}
}
Lenz, R. Processing and Presentation of 3-D volumes 1984 Proc. of the Swedish Society for Automated Image Analysis Symposium, Linköping  inproceedings  
BibTeX:
@inproceedings{Lenz1984a,
  author = {Reiner Lenz},
  title = {Processing and Presentation of 3-D volumes},
  booktitle = {Proc. of the Swedish Society for Automated Image Analysis Symposium, Linköping},
  year = {1984}
}
Lenz, R. Processing and Presentation of 3D-images 1984 Proc. of the International Symposium on Medical Images and Icons, Arlington, Virginia, USA  inproceedings  
BibTeX:
@inproceedings{Lenz1984,
  author = {Reiner Lenz},
  title = {Processing and Presentation of 3D-images},
  booktitle = {Proc. of the International Symposium on Medical Images and Icons, Arlington, Virginia, USA},
  year = {1984}
}
Lenz, R., Danielsson, P.-E., Cronström, S. and Gudmundsson, B. Presentation and Perception of 3D-images 1984 NATO-ASI, Pictorial Information Systems in Medicine, Braunlage, West-Germany  inproceedings  
BibTeX:
@inproceedings{Lenz1984b,
  author = {Reiner Lenz and Per-Erik Danielsson and Staffan Cronström and Björn Gudmundsson},
  title = {Presentation and Perception of 3D-images},
  booktitle = {NATO-ASI, Pictorial Information Systems in Medicine, Braunlage, West-Germany},
  year = {1984}
}
Lenz, R., Danielsson, P.-E., Crontstrom, S., Gudmundsson, B. and Edholm, P. Presentation and perception of 3D-images 1984 Seventh International Conference on Pattern Recognition (Cat. No. 84CH2046-1), pp. 749-51  inproceedings  
Abstract: Several methods for display of 3-D data are presented. Basic representations such as look-through projections and surface display are combined with stereo effects and interactively controlled motion to give a better 3-D impressions. The effects of various preprocessing steps are discussed
BibTeX:
@inproceedings{Lenz1984d,
  author = {Lenz, R. and Danielsson, P.-E. and Crontstrom, S. and Gudmundsson, B. and Edholm, P.},
  title = {Presentation and perception of 3D-images},
  booktitle = {Seventh International Conference on Pattern Recognition (Cat. No. 84CH2046-1)},
  publisher = {IEEE Comput. Soc. Press},
  year = {1984},
  pages = {749--51}
}
Lenz, R., Danielsson, P.-E. and Gudmundsson, B. Interactive display of 3D-images in PICAP II 1984
Vol. 507Proc. SPIE - Int. Soc. Opt. Eng. (USA), pp. 19-24 
inproceedings  
Abstract: The authors present some experiments in processing and display of true 3D-images (density volumes). The experiments have been carried out on the PICAP II image processing system
BibTeX:
@inproceedings{Lenz1984c,
  author = {Lenz, R. and Danielsson, P.-E. and Gudmundsson, B.},
  title = {Interactive display of 3D-images in PICAP II},
  booktitle = {Proc. SPIE - Int. Soc. Opt. Eng. (USA)},
  year = {1984},
  volume = {507},
  pages = {19--24}
}
Reinhardt, E., Blanz, W., Erhardt, R., Greiner, W., Hornstein, B., Kringler, W., Lenz, R., Schimpf, I., Schlipf, W., Schwarzmann, P., Strassle, G. and Bloss, W. Automated classification of cytological specimen based on multistage pattern recognition 1982 Proceedings of the 6th International Conference on Pattern Recognition, pp. 153-9  inproceedings  
Abstract: A prescreening system for the early detection of uterine cancer was developed. For the diagnosis of each input specimen (PAP-stained), a figure of malignancy has to be calculated automatically. Methods, problems and results of the whole project are summarized in this paper. Some thousand microscopic subfields of a specimen are successively scanned by an optimized TV-camera with high spatial resolution. The automated specimen analysis can be described by a two step procedure: single cell classification and evaluation of cell population. For the single cell classifier only features derived from the nuclear images are used. The pattern recognition procedures are based on a processor-oriented strategy, and can be adapted to other cytological specimen. The algorithms have been tested with 3.105 cell images of about 300 specimens
BibTeX:
@inproceedings{Reinhardt1982b,
  author = {Reinhardt, E.R. and Blanz, W.E. and Erhardt, R. and Greiner, W. and Hornstein, B. and Kringler, W. and Lenz, R. and Schimpf, I. and Schlipf, W. and Schwarzmann, P. and Strassle, G. and Bloss, W.H.},
  title = {Automated classification of cytological specimen based on multistage pattern recognition},
  booktitle = {Proceedings of the 6th International Conference on Pattern Recognition},
  publisher = {IEEE},
  year = {1982},
  pages = {153--9}
}
Reinhardt, E., Lenz, R., Greiner, W. and Schenk, U. Diagnostic Relevance of Visually non Suspect Cells for Cancer Diagnosis 1982 Int. Conf. High Resolution Cell Image Analysis, Los Angeles  inproceedings  
BibTeX:
@inproceedings{Reinhardt1982,
  author = {E.R. Reinhardt and R. Lenz and W. Greiner and U. Schenk},
  title = {Diagnostic Relevance of Visually non Suspect Cells for Cancer Diagnosis},
  booktitle = {Int. Conf. High Resolution Cell Image Analysis, Los Angeles},
  year = {1982}
}
Reinhardt, E., Schwarzmann, P. and Lenz, R. Satellite Image Analysis 1982 Solar Radiation Data Series F, Vol. 2, pp. 288-292  inproceedings  
BibTeX:
@inproceedings{Reinhardt1982a,
  author = {E.R. Reinhardt and P. Schwarzmann and R. Lenz},
  title = {Satellite Image Analysis},
  booktitle = {Solar Radiation Data Series F, Vol. 2},
  year = {1982},
  pages = {288--292}
}
Blanz, W., Lenz, R. and Reinhardt, E. Allgemeiner Ansatz zur Bildsegmentation 1981 DFG-Schwerpunktprogram Digitale Signalverarbeitung. Göttingen  inproceedings  
BibTeX:
@inproceedings{Blanz1981,
  author = {W.E. Blanz and R.L. Lenz and E.R. Reinhardt},
  title = {Allgemeiner Ansatz zur Bildsegmentation},
  booktitle = {DFG-Schwerpunktprogram Digitale Signalverarbeitung. Göttingen},
  year = {1981}
}
Reinhardt, E., Laub, G. and Lenz, R. Rekonstruktion von Schichtbildern mit Hilfe inkohärent-optischer Abbildungssysteme 1980 Tagung Erzeugung und Analyse von Bildern und Strukturen  inproceedings  
BibTeX:
@inproceedings{Reinhardt1980,
  author = {E.R. Reinhardt and G. Laub and R. Lenz},
  title = {Rekonstruktion von Schichtbildern mit Hilfe inkohärent-optischer Abbildungssysteme},
  booktitle = {Tagung Erzeugung und Analyse von Bildern und Strukturen},
  year = {1980}
}