Reiner Lenz

ABSTRACT This paper gives an overview of operator-based models that seem to be especially interesting for laser scanning microscopy. These methods were developed by Nazarathy et. al. in a series of papers about 10 years ago. In these papers they demonstrated that both the operators and Gaussian beams can be represented by matrices. We implemented the operator algebra in Mathematic and we also show by some simple examples how to analyze paraxial systems. A number of empirical experiments have also been performed to verify the validity of the model.

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.

In this paper we describe a novel compensation algorithm for color-weakness based on a new, objective criterion to compare normal observers and color-weak observers, using Riemann geometric properties of color spaces. The criterion is to match the color discrimination thresholds of average, normal observers and a colorweak observer. The method uses local and global isometry theory and provides the two groups of observers with the same color-difference experience. A one-dimensional compensation and simulation of color-weakness is shown as an application of the general approach to the Brettel color-blind model. The 2D and 3D compensations and simulations are illustrated in chromaticity planes and full color spaces.

We use methods from Riemann geometry to investigate transformations between the color spaces of color-normal and color weak observers. The two main applications are the simulation of the perception of a color weak observer for a color normal observer and the compensation of color images in a way that a color weak observer has approximately the same perception as a color normal observer. The metrics in the color spaces of interest are characterized with the help of ellipsoids defined by the just-noticable-differences between color which are measured with the help of color-matching experiments. The constructed mappings are isometries of Riemann spaces that preserve the perceived color-differences for both observers. Among the two approaches to build such an isometry, we introduce normal coordinates in Riemann spaces as a tool to construct a global color-weak compensation map. Compared to previously used methods this method is free from approximation errors due to local linearizations and it avoids the problem of shifting locations of the origin of the local coordinate system. We analyse the variations of the Riemann metrics for different observers obtained from new color matching experiments and describe three variations of the basic method. The performance of the methods is evaluated with the help of semantic differential (SD) tests.

ABSTRACT We extend a method for color weak compensation based on the criterion of preservation of subjective color differences between color normal and color weak observers presented in [2]. We introduce a new algorithm for color weak compensation using local affine maps between color spaces of color normal and color weak observers. We show how to estimate the local affine map and how to determine correspondences between the origins of local coordinates in color spaces of color normal and color weak observers. We also describe a new database of measured color discrimination threshold data. The new measurements are obtained at different lightness levels in CIELUV space. They are measured for color normal and color weak observers. The algorithms are implemented and evaluated using the Semantic Differential method.