Research On 3D Mesh Model Segmentation Method Based On Spectral Method

In recent years,with the rapid development of virtual reality technology,the processing of three-dimensional model data has attracted people's attention.3D mesh model segmentation,as a relatively basic step of 3D digital geometric model processing,has attracted more and more attention and research in recent years.In this paper,the segmentation of 3D mesh model is studied and discussed.Firstly,the research status at home and abroad is summarized and the previous algorithms are studied.Then two methods of 3D mesh model are proposed: the segmentation of 3D mesh model based on graph laplacian and the segmentation of 3D mesh model based on manifold harmonic basis(MHB).In order to improve the efficiency and effect of 3D mesh model segmentation algorithm.3D mesh model segmentation based on graph laplacian.The first step of segmentation is to extract the features of the model.This method needs to construct a graph laplacian matrix,which needs similarity matrix and degree matrix.In this paper,the method used to measure the information of points and patches in 3D mesh model is to define the weights between points by geodesic distance and angular distance,and then construct the similarity matrix to obtain the adjacency matrix and degree matrix.Then Laplacian matrix is constructed.Finally,the 3D mesh model is segmented by spectral clustering.Experiments show that this method can also achieve better visual segmentation effect for 3D mesh model.3D mesh model segmentation based on manifold harmonic basis.In recent years,Laplace operator has been frequently used in geometric processing applications.The characteristic equation of Laplace operator can reflect the essential characteristics of the 3D mesh model,and this operator can be relatively independent of the attitude change of the 3D mesh model.In this paper,a clustering algorithm based on manifold harmonic basis of grid Laplace operator is proposed to segment the 3D mesh model.Firstly,the discrete Laplace operator of 3D mesh model is computed,and the manifold harmonic basis of 3D mesh model is further obtained.Then,by decomposing the manifold harmonic feature,the corresponding eigenvalue equation is obtained to obtain the spectral embedding of the vertices of 3D mesh model,which makes the 3D mesh model normalized,thus avoiding the segmentation of 3D mesh model due to the change of attitude.Finally,the improved k-means clustering algorithm is applied to the normalized 3D mesh model to segment the feature vectors of the model,and the desired clustering cluster can be obtained,which can also achieve the segmentation of the 3D mesh model.Because the calculation of Laplace operator in 3D mesh completely abandons the way of geodesic distance,the Laplace matrix construction method of this method is significantly different from the first one.In fact,both methods extract the features of the 3D mesh model and map them to the spectral space,then process the data of the 3D mesh model with the theory of spectral embedding and spectral clustering.The difference is that the feature extraction methods of 3D mesh model are different.In the process of experiment,it is also found that different clustering segmentation numbers have great influence on the results of segmentation.At last,the SSE method is used to determine the optimal clustering segmentation number.