Research On Shape Correspondence Based On Compressed Manifold Model

In computer graphics and geometric application processing,shape correspondence is one of the most widely used fields.With the continuous development of Microsoft Kinect scanner and 3D technology,the shape correspondence is paid more and more attention in many application fields(such as molecular biology,mechanical engineering,medical image analysis).Finding the internal correspondence between 3D shapes can be applied to the fields of 3D scanning alignment,texture mapping,shape deformation and animation.At present,feature descriptors(thermonuclear feature descriptors,wave-kernel feature descriptors,curvature,etc.)and feature matching are mainly used to study the shape correspondence of 3D mesh models,but these methods cannot solve the self-symmetry problem of models,and the corresponding matching difference is likely to be too large.Because the current methods cannot find the corresponding vertex positions accurately,there is no good method to solve the local correspondence between 3D mesh models.Based on this,two new corresponding matching algorithms has been proposed based on the analysis and research of previous algorithms:One is to use the improved heat-kernel signatures to locally match the 3D mesh model;the other is to use the whole compression separation of the compressed manifold mode algorithm and combine the improved heat-kernel signatures and wave-kernel signatures to match the whole 3D mesh model.These two algorithms respectively correspond to the local and the global of the 3D mesh model,and at the same time the corresponding matching problem of the local and the global of the 3D mesh model has been solved.The main work of this paper is:(1)The improved heat-kernel signatures are used to locally match the 3D mesh model.heat-kernel signatures are feature descriptors in the 3D mesh model,the traditional heat-kernel signatures are calculated by discretizing Laplacian operator matrix.First,the Laplace operator matrix is decomposed to obtain the eigenvalues and eigenvectors of the 3D mesh model.Then,the heat-kernel eigenvalues of each 3D mesh model are calculated by using the heat-kernel signatures formula to find the true corresponding matching.In this paper,the Laplace operator is replaced by a discretized compressed manifold mode to improve the heat-kernel signatures.The compressed manifold mode is used to compress the local features of the mesh,and different local compression ranges can be obtained by setting the size of the eigenvector threshold.The experimental results show that compared with the original thermonuclear features,the improved thermonuclear features have a more accurate effect on calculating the local correspondence between 3D mesh models.(2)The 3D mesh model can be matched with the whole compression separation of the compressed manifold mode algorithm combined with the improved heat-kernel signatures and wave-kernel signatures.According to the existing theory,this paper proposes a new method to solve the corresponding matching of 3D mesh model,that is,the use of partial separation to calculate the whole.Firstly,a model is processed according to the traditional segmentation method,then the meaningful components of a model are separated,and then the whole correspondence is calculated by the gradual accumulation of each part.The segmentation method in this paper solves the problem of uneven segmentation of traditional methods,which is beneficial to the subsequent process of gradually calculating the overall correspondence through local separation of correspondence,and the algorithm has a higher accuracy rate.Compared with the existing algorithms,the algorithm in this paper solves the self-symmetry problem of the model and makes the corresponding matching effect better.The two methods studied in this paper are inseparable from the construction of the compressed manifold mode.One is to use the compressed manifold mode algorithm to separate the local features of the 3D mesh model to construct the correspondence of the local features.Compared with the traditional heat-kernel signatures matching results,the improved are more accurate.The other is to intercept and separate the parts through the compressed manifold mode,that is,to compress and separate the whole part of the model,and add each part correspondingly,so as to complete the matching of the whole model.Although the two models correspond to different regions,they both reflect the contributions and innovations of this paper respectively:(1)In this paper,the compressed manifold mode is extended to solve the local feature extraction,by improving the heat-kernel make the local correspondence of the model better;(2)In this paper,by using local separation of the compressed manifold model and combining the improve heat-kernel and wave-kernel for the overall correspondence of the non-rigid body model,it solves the problem of self-symmetry of feature descriptors,which makes the overall corresponding effect of the model better.