A New Method Of 3D Symmetric Shape Matching Based On Gromov-Wasserstein Distance

The matching problem of 3D non-rigid graphics has always been one of the key issues in the research and application fields of computer graphics,and the matching problem of symmetric graphics has always been a difficult problem.Existing methods have shortcomings such as low precision in symmetric point discrimination and long computational time.This paper proposes new solutions to these shortcomings.The main research contents of this thesis include: firstly,transform the graphic matching problem into a mathematical model optimization problem based on Gromov-Wasserstein distance,and propose a theothesisretical framework for the algorithm;Then,initial sampling is performed on the two input patterns to be detected to obtain their respective feature points,in order to accurately distinguish symmetric points from asymmetric points,this thesis uses the GromovWasserstein distance of the two feature point sets to distinguish the front,back,or top,and bottom of the pattern by adding information about sampling points at special locations;Further,aiming at the possible distortion of the graph,the geodesic distance matrix between feature points is transformed into a more intuitive euclidean distance matrix,thereby more accurately judging the left and right directions of the graph,avoiding symmetry confusion,and completing the initial layer matching of feature points;Finally,using a hierarchical matching algorithm based on geodesic distance can ultimately achieve dense matching.The algorithm in this paper is finally tested on TOSCA dataset,and compared with existing methods based on graph embedding,it has greatly improved matching accuracy and computational time.