3D Shape Similarity Measurement Based on Scale Invariant Functional Maps

Abstract

In recent years, the research focus on shape analysis has centered around the similarity and consistency of 3D models. The matching results derived from this analysis have broad applications in various fields, including shape retrieval and symmetry detection. Shape similarity measurement primarily encompasses feature extraction and distance calculation, with the challenge of effectively handling the non-rigid transformation of shapes. However, most existing shape similarity measurement methods neglect the scale invariance of shapes during feature extraction, rendering them unsuitable for the current task. In this paper, we propose the construction of a 3D signature called AvgSI, which is based on scale-invariant functional maps. AvgSI is a shape descriptor that leverages Laplace-Beltrami operators to efficiently extract geometric and topological information from 3D models. It is capable of extracting high-level features from multiple characteristics. By combining AvgSI with the scale-invariant BCICP (bijective and continuous Iterative Closest Point), we establish an effective pipeline for measuring the similarity of 3D models. This is achieved by calculating the correlation coefficient distance between the AvgSI values of the 3D shapes. Through comprehensive comparisons with the initial BCICP, our proposed method demonstrates stronger scale invariance, topological robustness, and isometric invariance. Results from a series of experiments validate the suitability of our framework for measuring the similarity of 3D models.