Analysis and Comparison of Real Functions on Triangulated Surfaces

The study of geometric and topological properties of a triangulated surfaceMis ubiquitous in geometry and shape processing. In these contexts, different techniques in research areas such as shape abstraction, comparison, and parameterization are based on the study of local properties of a mapping function f:M->R and that correspond to specific properties of the input shape. Therefore,it becomes interesting to analyze if two or more functions are "independent", that is, how much and where the measured properties differ. This paper proposes a set of descriptors to analyze, compare, and model a family of functions (M,f), when f varies.