Scaling Invariant Harmonic Wave Kernel Signature for 3D Point Cloud Similarity

Abstract

In recent years, the analysis tasks of 3D point cloud models have also attracted wide attention from researchers. The most basic and important research work of 3D point cloud model analysis is the similarity measurement of 3D models. The similarity measurement of 3D point cloud models are generally calculated by shape descriptors, which can capture the most unique features for 3D point cloud models. However, the traditional feature extraction methods for 3D point cloud models are less robust, only focus on rigid deformation and less attention to non-rigid deformation. Recent publications introduce the Laplace-Beltrami operator to define shape descriptors and analysis the non-rigid deformation of models. In this paper, a concise 3D point cloud descriptor is defined to describe the internal structure of 3D point cloud models: scaling invariant harmonic wave kernel signature (SIHWKS). SIHWKS is a shape descriptor involving in the Laplace-Beltrami operator, which can effectively extract geometric and topological information from 3D point cloud models. Based on SIHWKS, the modified Hausdorff distance between SIHWKS values of 3D point cloud model is calculated as similarity measurement, which provides an effective method for 3D point cloud model analysis. Lastly, experiments conducted on public 3D shape datasets show the SIHWKS has the advantages of isometric invariance, scaling invariance and it is robust to topology, sampling and noise.