Publikationen nach Jahren

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and -functions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel.

This special issue has its origin in the NASAGEM 07 workshop that took place in October 2007, held as part of a sequence of events including the HAPTEX 07 workshop and the Cyberworlds 07 conference.

Wir stellen ein neuartiges, semi-immersives VR-System vor, welches neben visuellem auch haitisches Feedback in einem grossen Arbeitsbereich ermöglicht. Stichworte: VR-System, Haptik, verteilte Systeme

In this work we describe the behavior of electrical circuits by a mixture of algebraic and differential equations. We show how to use a geometric interpretation and geometric algorithms to explicitly compute operation points for a special class of electronic circuits. To that end, we discuss how to trace curves on folded manifolds.

Theoretical aspects of circuit equations from a differential geometric point of view are considered and methods for solving circuit equations by means of algorithms from computational differential geometry are presented. These methods are illustrated by means of some simple circuit examples.