Curve reconstruction, the traveling salesman problem and Menger's theorem on length
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Three-Dimensional Face Recognition
International Journal of Computer Vision
Geometric accuracy analysis for discrete surface approximation
Computer Aided Geometric Design
Sampling and Reconstruction of Surfaces and Higher Dimensional Manifolds
Journal of Mathematical Imaging and Vision
Curvature based clustering for DNA microarray data analysis
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part II
Isometric Embeddings in Imaging and Vision: Facts and Fiction
Journal of Mathematical Imaging and Vision
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We consider the problem of better approximating surfaces by triangular meshes. The approximating triangulations are regarded as finite metric spaces and the approximated smooth surfaces are viewed as their Haussdorff-Gromov limit. This allows us to define in a more natural way the relevant elements, constants and invariants, such as principal directions and Gauss curvature, etc. By a "natural way" we mean intrinsic, discrete, metric definitions as opposed to approximating or paraphrasing the differentiable notions. Here we consider the problem of determining the Gauss curvature of a polyhedral surface, by using the metric curvatures in the sense of Wald, Menger and Haantjes. We present three modalities of employing these definitions for the computation of Gauss curvature.