Eye movements and information geometry.

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 Levý flights, have been used in these investigations.

Modeling, Measuring, and Compensating Color Weak Vision.

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-noticeable-differences between the colors which are measured with the help of color-matching experiments.

Color-weak compensation using local affine isometry based on discrimination threshold matching.

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.

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.

Octahedral transforms for 3-D image processing.

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.

Evaluation and unification of some methods for estimating reflectance spectra from RGB images.

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.

Two stage principal component analysis of color.

We introduce a two-stage analysis of color spectra. In the first processing stage, correlation with the first eigenvector of a spectral database is used to measure the intensity of a color spectrum. In the second step, a perspective projection is used to map the color spectrum to the hyperspace of spectra with first eigenvector coefficient equal to unity.

Calibrating color cameras using metameric blacks.

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.

Statistical properties of color-signal spaces.

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).