Herbert Edelsbrunner

TL;DR: The authors' computeraided classification system could provide effective recognition of three main types of gastric mucosal patterns and thus may lead to pathology predict ion and supporting of clinical decision.

TL;DR: The Yaroslavl International Conference on Discrete Geometry dedicated to the centenary of A.D. Alexandrov was organized by the International B.N. Delaunay Laboratory "Discrete and Computational Geometry" and took place from August 13 to 18, 2012 at the P.G. Demidov YaroslavL State University.

TL;DR: In this paper, the densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices were studied, and it was shown that the minimum is attained for the Delaunain triangulation if this is the case for finite sets.

TL;DR: In this article, the authors survey the methods and results obtained with discrete Morse theory, and discuss some of its shortcomings, using simulations to illustrate the results and to form conjectures, obtaining numerical estimates for combinatorial, topological and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics.

TL;DR: In this paper , the Dehn-Sommerville relations for convex polytopes were extended to sublevel sets of the depth function, and they were used to extend the expressions for the number of faces of neighborly polytes to the 5 number of cells of levels in neighborly arrangements.