| Non-rigid 3D motion reconstruction is mainly studies the information provided from a set of 2D moving image sequences to recover it’s 3D structure matrix and the motion matrix of the camera.Early research is based on the factorization of the observation matrix decomposition,combined with the linear combination method to represent the non-rigid 3D structure with the shape basis and the correlation coefficient matrix.In recent years,with the proposed shape-trace space duality theory,the study of non-rigid 3D motion reconstruction is introduced into the trajectory space,and non-rigid 3D structure is reconstructed by the linear combination of trajectory bases,this method overcomes the difficulties of shape basis species selection and the complexity of the solution.At the same time,this method has the problem of the choice of the trajectory basis and the selection of the size.With the idea of the sparse representation,we use a series of sparse matrix coefficients to automatically select the trajectory base unit to approximate the real trajectory curve,so as to avoid the selection of the basis size.However,there are some problems such as the optimal selection of the trajectory atoms and the optimization of the structure matrix and the selection of the optimal basis in the sparse approximation.In view of these problems,this paper does the following work based on sparse representation.(1)In order to solve the problem of the best choice of trajectory base atom and the optimization of the structure matrix,this paper introduces an orthogonal matching pursuit and accelerated proximal gradient algorithm(OMP-APG).Firstly,the trajectory basis coefficients are solved by orthogonal matching pursuit algorithm with the idea of "maximization approximation" of sparse representation;Then,the non rigid 3D structural matrix is reconstructed with the predefined trajectory basis;Finally,considering the non-rigid 3D structure matrix is a low rank matrix,the rank minimization problem is relaxed to the nuclear norm minimization problem,and the structure matrix is optimized by the accelerated proximal gradient algorithm.The sparse representation can reduce the computational complexity of large matrix,and the optimalcombination of trajectory bases can be selected adaptively by a set of sparse coefficients,which overcomes the shortcomings of artificially determining the number of trajectory bases,and obtains more accurate 3D reconstruction effect.In this paper,experiments on different non rigid motion models show that the algorithm can effectively improve the reconstruction accuracy of non rigid bodies.(2)For the problem of selection and optimization of the basis functions,this paper proposes a 3D reconstruction of non-rigid bodies based on over-complete dictionary learning in combination with dictionary learning theory and sparse representation.Non-rigid motion tends to show the complexity and diversity,so single orthogonal basis or a combination of pure basis is not very good to represent the feature point trajectories,which leads to its 3D structure reconstruction is not accurate.This paper uses the method of dictionary learning,combined with the atoms of non coherent constraints,through orthogonal matching pursuit algorithm for solving the trajectory coefficient of basis function(now called a dictionary)is also updated to solve.The dictionary,which can be obtained by this way,is rich in atomic species,so it can be diversified to represent the trajectory of the feature points,which can improve the reconstruction accuracy and get better reconstruction results. |
