Robustness and modularity of 2-dimensional size-functions functions - An experimental study

This paper deals with the concepts of 2-dimensional size function and 2-dimensional matching distance. These are two ingredients of (2-dimensional) Size Theory, a geometrical/topological approach to shape analysis and comparison. 2-dimensional size functions are shape descriptors providing a signature of the shapes under study, while the 2-dimensional distance is the tool to compare them. The aim of the present paper is to validate, through some experiments on 3D-models, a computational framework recently introduced to deal with 2-dimensional Size Theory. We will show that the cited framework is modular and robust with respect to noise, non-rigid and non-metric-preserving shape transformations. The proposed framework allows us to improve the ability of 2-dimensional size functions in discriminating between shapes.