Scale-Invariant Heat Kernel Mapping

In shape analysis, scaling factors have a great influence on the results of non-rigid shape retrieval and comparison. In order to eliminate the scale ambiguity in shape acquisition and other cases, a method with scale-invariant property is required for shape analysis. The mapping method previously proposed only preserves geodesic distances between pair wise points. In this paper, a Scale-invariant Heat Kernel Mapping (SIHKM) method is introduced, which bases on the Scale-invariant Heat Kernel (SIHK) that handles various types of 3D shapes with different kinds of scaling transformations. SIHK is the generalization of the Heat Kernel and related to the heat diffusion behavior on shape. By using the SIHK, we retrieve intrinsic information from the scaled shapes while ignoring the impact of their scaling. SIHKM method maintains the heat kernel between two corresponding points on the shape with scaling deformations, including scaling transformation only, isometric deformation and scaling, and local scaling on shapes. The proof of the theory and experiments are given in this work. The experiments are performed on the TOSCA dataset, which show that our proposed method achieves good robustness and effectiveness to scaled shape analysis.