Scale-Invariant Heat Kernel Mapping for Shape Analysis

In shape analysis, scaling factors have a great influence on the results of non-rigid shape retrieval and correspondence. In order to eliminate the effects of scale ambiguity, a method with scale-invariant property is required for shape analysis. Previous mapping method only focus on the isometric conditions. In this paper, a Scale-invariant Heat Kernel Mapping (SIHKM) method is introduced, which bases on the heat diffusion process on shapes. It is capable of handling various types of 3D shapes with different kinds of scaling transformations. SIHKM is the extension of the Heat Kernel and related to the heat diffusion behavior on shapes. With SIHKM, we will obtain the intrinsic information from the scaled shapes while without regard to the impact of their scaling. SIHKM method maintains the heat kernel between two corresponding points on the shape with scaling deformations. These deformations include scaling transformation only, isometric deformation and scaling, and local scaling on shapes. The proof of the theory and experiments are given in this work. All experiments are performed on the TOSCA dataset and the results show that our proposed method achieves good robustness and effectiveness for scaled shape analysis.