Geometrical characterization of textures consisting of two or three discrete colorings

Abstract

Geometrical characterization for discretized contrast textures is realized by computing the Gaussian and mean curvatures relative to the central pixel of a clique and four neighboring pixels, these four neighbors either being first or second order neighbors. Practical formulae for computing these curvatures are presented. Curvatures based on the central pixel depend upon the brightness configuration of the clique pixels. Therefore the cliques are classified into classes by configuration of pixel contrast or coloring. To look at the textures formed by geometrically classified cliques, we create several textures using overlapping tiling of cliques belonging to a single curvature class. Several examples of hyperbolic textures, consisting of repeated hyperbolic cliques surrounded by non-hyperbolic cliques, are presented with the nonhyperbolic textures. We also introduce a system of 81 rotationally and brightness shift invariant geo-cliques that have shared curvatures and show that histograms of these 81 geo-cliques seem to be able to distinguish isotrigon textures.