A Scale-Invariant Diffusion Distance for Non-rigid Shape Analysis

Diffusion geometry has been adopted in various shape processing applications, ranging from pattern recognition to more recent 3D shape analysis. But scaling factors have a great influence on the results of non-rigid shape processing such as shape retrieval, correspondence and comparison. There remains a difficult challenge for shape processing without a priori knowledge of the scale of the input shapes. In this paper we address the scale ambiguity problem with a new distance measure called Scale-invariant Diffusion Distance (SIDD). This SIDD is the extension of the diffusion distance, and has all the properties inheriting from it. Comparing to some existing distances, the scale-invariant diffusion distance is more suitable for the non-rigid shape analysis. Moreover, the proposed algorithm is simple and easily implement able. The proof of theory is given and some experiments are done on the TOSCA dataset. The results of the experiments show that our method achieves good robustness and effectiveness in scaled shape analysis.