3D Shape Matching Based On The Graph Structure Information Constraint Non-rigid Deformation

Shape matching is a fundamental problem in computer vision,computer graphics,and pattern recognition,given its key role in many applications such as shape retrieval,surface reconstruction,and skeletal analysis.The primary purpose of matching is to find a meaningful correspondence between feature points from two matching shapes.Based on the correspondence,various practical applications are realized.At present,for the difference of shape deformation,the shape matching methods can be divided into two categories: the matching method for rigid deformation and the matching method for non-rigid deformation.For the rigid deformation model,most of the methods are to formulate the shape matching problem as a linear assignment problem,and the objective function is solved by using the combinatorial optimization solution method such as Hungarian algorithm,and Auction algorithm.For the non-rigid deformation model,most of the methods are to formulate the shape matching problem as a quadratic assignment problem,and the objective function is solved by using optimization method such as convex relaxations or difference of convex functions programming.However,when the shapes exhibit significant variation in poses,surface details,and topological shortcuts,the similarity measures of shapes become irrelevant,thereby making the matching problem especially difficult to solve.Therefore,we mainly improve the accuracy of shape matching problem by modifying the optimization algorithm,increasing the deformation constraint,and improving the descriptiveness of the assignment matrix.This paper proposes a matching method based on graphical structure information and Reweighted Random Walks.The algorithm mainly uses the shape context descriptor to constrain the random walk,which can affect the random walk probability matrix to make the algorithm more robust and accurate.We calculate the bias matrix by using descriptor and then in the iteration we use it to enhance the accuracy of random walks and random jumps,finally we get the matching result by discretization of the matrix.The algorithm not only preserves the noise robustness of reweighted random walks but also possesses the rotation,translation,scale invariance of shape contexts.Through extensive experiments on real images and random synthetic point sets,and compared with other algorithms,we confirmed that thismethod can produce excellent results in shape matching.This paper proposes a shape matching method based on the combination of three types of graphics structure information.The method achieves automatic dense registration and can match two three-dimensional models under isometric or near-isometric transforms and non-rigid deformations.The method includes three major steps: first,the vertices are described based on three types of graphic structure information,namely Euclidean structure information,Riemannian structure information,and conformal structure information.Second,the matching problem is formulated as an optimization problem,and a novel objective function is proposed.Third,the optimal solution is computed by solving the objective function using the projected descent optimization procedure.We demonstrates the superior performance of the algorithm by conducting extensive quantitative and qualitative evaluations on several challenging shape matching datasets.This paper proposes a shape matching method based on graph structure information constraint deformation.Since volumetric data tends to have large resolutions,the method of constructing the distribution matrix requires a lot of time complexity and space complexity.Therefore,we propose a novel registration method for volumetric data.The input of the algorithm is a healthy skeletal model,and a pathological skeletal model.Due to the inherent defects of CT scanning instruments,the input data will be different in position,direction,and scale.Therefore,in order to improve the accuracy of the algorithm,we first performed the initial alignment with the help of feature point constraints,and then the volume registration combining local deformation and registration is performed.The data used in this experiment was derived from CT scan data of real humans.By analyzing the experimental results and comparing with other algorithms,we prove the accuracy and robustness of the proposed method.