Size functions for comparing 3D models

This paper proposes an original framework to bring size functions to the 3D context. Size functions are introduced here for the first time to discriminate among 3D objects represented by triangle meshes, through the proposal of a method for defining size graphs independently of the underlying triangulation. We first derive a skeletal signature, which guarantees the topological coding and the geometric description of an object surface, then this signature is used as a size graph to compute discrete size functions, which readily give a similarity measure between shapes. The result is the introduction of a new technique for 3D model retrieval, devised to capture both local and global properties of a shape. We demonstrate the potential of our approach in a set of experiments, and discuss the results with respect to existing techniques.