"Shape-Curvature-Graph": Towards a New Model of Representation for the Description of 3D Meshes

This paper presents a new shape descriptor for 3D meshes, that aims at representing an arbitrary triangular polyhedron using a graph, called SCG for “Shape-Curvature-Graph”. This entity can be used to perform self-similarity detection, or more generally to extract patterns within a shape. Our method uses discrete curvature maps and divides the meshes into eight categories of patches (peak, ridge, saddle ridge, minimal, saddle valley, valley, pit and flat). Then an adjacency graph is constructed with a node for each patch. All categories of patches cannot be neighbors in a continuous context, thus additional intermediary patches are added as boundaries to ensure a continuous consistency at the transitions between areas. To validate the relevance of this modular structure, an approach based of these shape descriptor graphs is developed in order to extract similar patterns within a surface mesh. It illustrates that these “augmented” graphs obtained using differential properties on meshes can be used to analyze shape and extract features.