A new Combinatorial Ricci curvature and Laplacian operators for grayscale images are
introduced and tested on 2D synthetic, natural and medical images. The effectiveness of the …

We present a geometric representation of a tetrahedral mesh that is solely based on
dihedral angles. We first show that the shape of a tetrahedral mesh is completely defined by …

Gauss-Bonnet for simple graphs G assures that the sum of curvatures K (x) over the vertex
set V of G is the Euler characteristic X (G). Poincare-Hopf tells that for any injective function f …

We prove Gauss-Bonnet and Poincare-Hopf formulas for multi-linear valuations on finite
simple graphs G=(V, E) and answer affirmatively a conjecture of Gruenbaum from 1970 by …

A discrete version of the Ricci flow, applicable to images, is introduced and applied in image
denoising and in single-image-based enhancement and super-resolution. This flow is …

Combinatorial Ricci flow on an ideally triangulated compact 3-manifold with boundary was
introduced by Luo as a 3-dimensional analogue of Chow-Luo's combinatorial Ricci flow on a …

Radiological imaging of the prostate is becoming more popular among researchers and
clinicians in searching for diseases, primarily cancer. Scans might be acquired with different …

If G is the category of finite simple graphs G=(V, E), the linear space V of valuations on G has
a basis given by the f-numbers vk (G) counting complete subgraphs Kk+ 1 in G. The …

Geometric structures are natural structures of surfaces, which enable different geometries to
be defined on the surfaces coherently and allow general planar algorithmic constructions to …