The Statistical Methods For Robust Point Set Matching

Point set matching is to establish the matching correspondences between point sets,which is the foundation of point set registration and image registration.And the feature extraction,feature description and feature matching are its key steps.In practical applications,the existence of deformation and outliers seriously affects the matching performance which results from the variation of image quality and the inaccuracy of feature extraction methods.So it is imperative to develop the robust point set matching methods.In the field of computer vision and pattern recognition,the research on the robust and fast point set matching methods based on probability statistics and graph theory has attracted the attention of scholars.Among them,the point set matching method based on mixture models is one of the research hotspots,which skilfully converts the feature matching to a probability density estimation problem based on mixure models.However,this kind of methods may be prone to producing mismatches when there is large deformation or a large number of outliers in the point set.Based on this point,this paper studies the statistical method for robust point set matching.The main research works and innovation points include the following:(1)Due to the impact of the noise and deformation in the feature extraction,the salient point extraction method and local structural despcription method for image registration are proposed based on Salient Image Disk(SID)feature extraction method.One is to extracte stable affine-invariant features after repetition detection in multiple images generated by the Non-subsampled Contourlet Transformation(NSCT).The other is that a local structure description method using Local Self-Similarity(LSS)descriptor is proposed.And then the proposed methods are applied to the registration problem of the Synthetic Aperture Radar(SAR)images,and the experimental results confirm the validity of the two methods.(2)For the mismatches caused by the point set matching method based on coherent point drift(CPD)when treating the point sets with a lot of outliers,a point set matching method is proposed based on an adaptive mixture model.In the construction of Gaussian Mixture Model(GMM),the proposed method combines the proximity of spatial location information and similarity of local attribute information of features.And the adaptive updating formula of weight coefficient is derived.Finally,the iterative algorithms for affine and non-rigid point set matching are established.The experimental results on simulated point set and real images indicate the proposed method is superior to the point set matching method based coherent point drift in accuracy and robustness.(3)To improve the robustness to oultiers,a robust point set matching method is proposed based on the Student's-t Mixture Model(SMM),where the point set matching is modeled as a probability density estimation problem using the Student's-t Mixture Model.Based on the Bayesian statistical methods,the variational inference is used to estimate the variational posteriors of model variables and an efficiently iterative updating algorithm is derived.For non-rigid point set matching problem,it can adaptively update the regularization parameter during the matching process.The experimental results on on simulated point sets and real images verify the robustness of the proposed method.(4)For the preservation of the geometric structures in the point set matching method based on Student's-t Mixture Model,a geometric structure preserving model of point set matching is proposed.The constraints of global regularization and Laplacian manifold regularization are enforced through the prior distribution.Finally,we derive an efficient algorithm,where the simulated annealing strategy is used to update the regularization parameters gradually reducing the influence of regularization terms in the matching process.Experimental results show that the proposed method can significantly improve the matching performance when treating the matching problem in the existence of the non-rigid deformation and great difference in structure.