3D Model Retrieval Method Based On Persistent Homology

In the discipline of computer simulation,the application of 3D model occupies the most important position.With the increasing number of 3D models year by year,how to retrieve 3D model quickly and effectively starts to arouse the discussion of many researchers,and various 3D model retrieval technologies also emerge at the right moment.In this paper,a 3D model retrieval method based on persistent homology is proposed.Firstly,this method uses the persistent homology principle in topological data analysis to extract the feature descriptors of the 3D model.Secondly,the persistence diagram is embedded into a high-dimensional space through the persistence weighted Gaussian kernel function to measure the similarity,and verify the feasibility of the algorithm in the similarity measurement of the persistence diagram.Finally,it uses the traditional bottleneck distance and the improved Wasserstein distance algorithm to measure similarity,and the two algorithms are compared.The main work of this article is as follows:(1)The feature descriptor of 3D model is extracted by using the principle of persistent homology.In this paper,the persistent homology principle in algebraic topology is used to obtain the topology structure of the 3D model in different scales and record its life cycle,from which stable topology invariants are extracted and expressed in the persistence diagram,which are taken as the feature descriptors of the model.The feature descriptors extracted by this method have stability and scale invariance,which fully and effectively represent the topological features of the 3D model.In this paper,experiment is performed on the data set SHREC TRACK 2011,and the one-dimensional Betti number of the 3d model in the process of persistent homology was extracted.(2)Research on persistence weighted Gaussian kernel function on persistence diagram.By using a statistical framework for multiple persistence diagrams,a measurement algorithm based on persistence weighted Gaussian kernel function is proposed in this paper.By this algorithm,the persistence diagram of discrete metrics is embedded in the regenerated Hilbert space through the Gaussian kernel function,and weights are given to the persistence effects of each topology feature in the persistence diagram.The inner product between two persistent diagrams,and the distance between high-dimensional vectors is calculated according to the inner product,so as to obtain the similarity between the two persistent diagrams.The experimental results show that the persistence weighted Gaussian kernel function can realize the similarity measurement on the persistence diagram and achieve the goal of 3D model retrieval.(3)Research on improved Wasserstein distance algorithm.In this paper,an improved Wasserstein distance algorithm is used to measure the similarity between the persistent diagrams.This algorithm projects two-dimensional points in the persistent diagram into onedimensional points in different directions and obtains one-dimensional Wasserstein distance in each direction,the cumulative sum of them and the average is the final distance.Then the improved Wasserstein distance algorithm is compared with the traditional bottleneck distance algorithm.The experimental results show that the improved Wasserstein distance algorithm can achieve the similarity measurement between 3D models.Compared with the traditional bottleneck distance algorithm,the algorithm significantly improves the effectiveness and accuracy of 3D model retrieval.