3D Shape Matching Based On Gromov-wasserstein Distance

With the rapid development of science technology and the improvement of 3Dtechnology,great progress has been made in the field of data acquisition and shape modeling.There are many application fields based on numerical analysis,such as molecular biology,face identification,pattern recognition and so on.Shape matching is one of the fundamental problems in Computer Graphics,Computer Vision and so on,which is to find corresponding points on two pieces of geometry.It includes rigid and non-rigid matching,isometric matching,conformal matching,or general mappings between two surfaces.In this paper,we mainly do research on the non-rigid matching problem.In this paper,Gromov-Wasserstein(G-W)distance is proposed as a new method to perform shape matching in order to improve the matching rate and precision.First,the two shapes are embedded into the metric measure space.Based on G-W distance,the objective function and constraint condition can be constructed after generating samples via farthest points sampling.This is a NP-hard QAP problem.In order to solve the problem,we propose a group of linear systems via the relaxation of constraint to make the model easy and authentic based on the analysis of the matching problem.After conducting the projected gradient approach,we get the solutions,which are more accurate and greatly closer to the theoretical value.Not only can it improve the matching precision,but also increase the matching rate.Experimental results on the SHER’10 data set demonstrate that our method is superior to state-of-the-art methods.