Reiner Lenz

Three-dimensional microscopy using a confocal laser scanning microscope

In a scanning laser microscope detecting fluorescent light from the specimen, the depth-discriminating property of confocal scanning has been used to carry out optical slicing of a thick specimen. The recorded digital images constitute a three-dimensional raster covering a volume of the specimen. The specimen has been visualized in stereo and rotation by making look-through projections of the digital data in different directions. The contrast of the pictures has been enhanced by generating the gradient volume. This permits display of the border surfaces between regions instead of the regions themselves.

Group theoretical methods in image processing

Preliminaries.- Representations of groups.- Representations of somes matrix groups.- Fourier series on compact groups.- Applications.

Evaluation of methods for shaded surface display of CT volumes

Abstract There are several ways to compute a shaded surface display of radiological 3D density volumes. In this paper we evaluate 12 methods which are different combinations of principles for detection of the surface to be displayed (gray-value threshold, gradient threshold, zero-crossing of 2nd derivative), localizing this surface in space (grid-point accuracy, subvoxel accuracy) and finally estimating the direction of the surface normal (from the gradient in the 213 depth image, from the gradient in the 3D-volume). The best quality is obtained by zero-crossing detection, subvoxel localization, and 3D-gradient orientation.

Efficient Invariant Representations

Invariant representations are frequently used in computer vision algorithms to eliminate the effect of an unknown transformation of the data. These representations, however, depend on the order in which the features are considered in the computations. We introduce the class of projective/permutation p2-invariants which are insensitive to the labeling of the feature set. A general method to compute the p2-invariant of a point set (or of its dual) in the n-dimensional projective space is given. The one-to-one mapping between n + 3 points and the components of their p2-invariant representation makes it possible to design correspondence algorithms with superior tolerance to positional errors. An algorithm for coplanar points in projective correspondence is described as an application, and its performance is investigated. The use of p2-invariants as an indexing tool in object recognition systems may also be of interest.

Unsupervised filtering of color spectra

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. Systems consisting of positive weight vectors are then approximated with Gaussian quadrature methods. In the experimental part of the paper we investigate the properties of three databases consisting of reflectance spectra. We compare the statistical structure of the different databases and investigate how these systems can be used to explore the structure of the space of reflectance spectra.

Light scattering and ink penetration effects on tone reproduction.

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 Rp(o) of the substrate paper, the transmittance Ti of the ink layer, the parameter gamma 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 images being viewed as more saturated in color.

Point configuration invariants under simultaneous projective and permutation transformations

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 ( p 2 ) invariants of the four collinear and the five coplanar points configurations. The p 2 -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 p 2 -invariants yield a significant speedup. Permutation invariants for affine transformations are also discussed.

Group invariant pattern recognition

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.

Generalized co-occurrence matrix for multispectral texture analysis

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.

Modified Gradient Search for Level Set Based Image Segmentation

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.