The Research On 3D Non-rigid Structure From Motion Based On Shape-trace Fusion Constraints

Non-rigid reconstruction from motion is a key technology for computer to display the objective world virtually.It focuses on how to recover the rotation information and the 3D structure of non-rigid from a given set of 2D dynamic image sequences.There are two major reconstruction schemes: the 3D reconstruction in the shape space and reconstruction in the trajectory space.The reconstruction based on shape space is simple and convenient.However,in the process of reconstruction,new shape basis are reconstructed for all different sequences,leading to a large number of variables,which makes the algorithm complex and limited in scope of application.Although the reconstruction based on the trajectory basis method solves the limitation of the above-mentioned,the number and type of predefined trajectory basis in this method are hard to choose.The selection of basis atoms too large or too small is not conducive to accurate reconstruction.In order to solve the problem that the shape-based reconstruction method contains numerous variables and needs complicated operation,and how to choose the number and types of radical atoms in the trajectory-based method,a reconstruction method based on multi-constraint fusion is proposed and better reconstruction effect is obtained.This method has low computational complexity and high universality.In this regard,based on the shape-track duality space,this thesis is summarized as follows:(1)A more accurate rotation matrix of camera is obtained.Combining the orthogonal constraint that satisfies correction matrix with the trace minimization constraint of Gram matrix,the semi-positive definite programming packet is used to obtain the matrix.Once the correction matrix has been restored,the accurate rotation matrix of camera is obtained.The accurate rotation is applied as an initial condition to solve the structure matrix,and the accurate rotation results have an important influence on accuracy of the structure matrix.(2)For the problem that the number and types of bases are difficult to choose in trajectory space,this thesis presents a method that directly imposes smooth constraints on trajectories.By defining the smoothing matrix and establishing the minimum objective function of trajectory velocity and acceleration residual error,the closed optimal analytical solution is derived.There is no need to introduce any predefined base information so as to avoid the limit of the selection.The proposed continuity constraint is the essential constraint of trajectory space,so it is more general and adaptive,the algorithm is simple and the computational complexity is low.Experiment results on different motion models show that the reconstruction accuracy and robustness of the motion model is improved effectively.(3)In order to improve the accuracy of reconstruction,a method based on shape-trace multi-constraint fusion is proposed.Firstly,aiming at the low rank property of structure matrix,a more compact low-rank constraint is analyzed by matrix permutation,and a new objective function is obtained by combining low-rank constraints with the smooth constraints on trajectories.Finally,the alternating direction multiplier method is used to solve the function.The proposed trajectory smoothing constraints and the compact low-rank constraints are all essential constraints of non-rigid motion.Experiment results show that the proposed method is highly applicable and obtains higher reconstruction accuracy.