Size Functions for Comparing 3D Models

This paper proposes an original framework to use size functions in the 3D context. Size functions are a mathematical tool, that have already shown its effectiveness for image retrieval and classification. They 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. The attractive feature of size functions is that it readily gives 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. Finally, we demonstrate the potential of our approach in a set of experiments, and discuss the results with respect to existing techniques.