The 3D Shapes Isometric Deformation Based On Stochastic Neighbor Embedding

Researches of three-dimensional shapes has experienced decades of development,and achieved substantial achievement.It has provided a great convenience in many fields such as three-dimensional games,medical research,three-dimensional printing,etc.But the study of complex nonrigid shapes still has certain challenge.The nonrigid shapes are considered to have the same isometric deformation.So,we use the inner distance to describe the isometric geometric structure.The inner distance of three-dimensional shapes is the length of the shortest path in the interior of any two points.Stochastic neighbor embedding algorithm is a manifold mapping method to measure the degree of similarity by using probability tools.The manifold mapping method is applied to the three-dimensional shapes,and the Euclidean distance of the high dimensional space is replaced by the inner distance to realize the isometric deformation and obtain the standard-models.This paper mainly focuses on the following aspects:Firstly,this paper introduces stochastic neighbor embedding algorithm SNE,t-SNE,researches stochastic neighbor embedding Ca-tSNE based on Cauchy distribution and SKL-tSNE based on symmetric KL divergence.Secondly,the extraction of 3D shape distance feature is introduced in detail,including the calculation of 3D inner distance based on voxel and the extraction of feature points.Thirdly,stochastic neighbor embedding algorithms are applied to the three-dimensional isometric deformation to verify the effectiveness and advantages of each algorithm in 3D shape deformation.This paper mainly takes a lot of research on 3D shape deformation in the TOSCA,as well as the SHREC07 graphics library.It is found that t-SNE algorithm based on inner distance in 3D isometric deformation has achieved good effect.Ca-tSNE based on Cauchy distribution is more flexible on 3D shape deformation,and selecting the appropriate scale parameter can get the optimal deformation effect.SKL-tSNE based on symmetric KL divergence has no effect on 3D shape deformation.