Research On Graph Matching Methods Based On High-order Tensor

It is a fundamental problem in computer vision to establish correspondences between two sets of visual features.Graph matching method uses graph structure to describe the geometric relationship between features and the matching algorithm is used to determine correspondences between features.It has important research significance both in mathematical research and practical applications such as image matching,image reconstruction,target tracking.Firstly,this thesis makes a detailed research on the current state and development trend of graph matching problem and summarizes the research difficulties and trends of this problem.To deal with these difficulties,this thesis studies the problem of graph matching based on high-order tensor from four aspects,and proposes novel graph matching methods:(1)Considering the binary discrete property of the assignment matrix in the graph matching problem,this thesis adds a Shannon entropy barrier function to the hypergraph matching model,so that the solution poesses binary discrete property,which avoids from the uniform value of assignment matrix obtained by existing methods.This model is solved by an nonmonotone active set Newton method.(2)Generally,the traditional graph matching problems describe the geometric relationship between feature points from the global perspective,but neglect the local information.Since the fuzzy relaxation graph matching method uses local information which brings more geometric information to the model to determine the correspondence of features,this thesis extends it to a hypergraph matching one,and uses stricter constraints of feature points to improve the effect of graph matching algorithm.The model is dealt with by the box constrained augmented Lagrangian method to split the problem into subproblems which are easier to be solved,and the subproblems are solved by L-BFGS-B method.(3)Since the assignment matrix of the graph matching problem is sparse,from the perspective of sparse optimization,this thesis introduces LP regularization method into the hypergraph matching model,so that the solution results poesses sparse property,and it is solved by an adaptive nonmonotone spectral projected gradient method.Due to the much more complex geometric relationship of 3D feature points,this thesis introduces sparse optimization,meanwhile uses a three-dimensional hyperedge structure to describe the geometric relationship between feature points more accurately,and designs a new feature vector for 3D feature points.The model is solved by an nonmonoton spectral gradient projection method whose line search is modified by an adptive one.Experiments with other compared methods are conducted to verify the performance of our method,and the experimental results show that our method outperforms among the compared methods.Finally,a brief summary of the thesis and the furture works about graph matching are presented.