The Research On 3D Non-rigid Structure From Motion Based On Sparse Approximation

Non-Rigid Structure from Motion(NRSfM) referred to the process of recovering the 3D structure of the object from a set of feature point sequences in photos. The research of NRSfM problem was based on the matrix factorization algorithm. Then the motion structure of the object could be recovered by shape basis method or trajectory basis method. At first shape basis method was proposed to solve the NRSfM problem. But this method needed to construct different shape basis when dealing with different NRSfM problem, it was so limited that it could not fully satisfy the conditions of NRSfM problem. Trajectory basis method, proposed to replace the shape basis method because of the duality existed in these two methods, was used to recover the motion structure by reconstructing the trajectory curves of the motion object other than using the shape basis. This method solved the limitation problem of the shape basis well. But there still existed some problems in trajectory basis method when pre defining the trajectory basis function. First of all, the trajectory basis used in trajectory basis method was only a little part of the full trajectory basis matrix defined be the basis function, so it was a key problem to determine a suitable size number of the trajectory basis. If the size number was too small, it might miss many details of the motion trajectory curves and lead to a big structure error. However, if the size number was too big, it would be a big problem in computing and might lead to a NP-hard problem. The second problem was the selection of the trajectory basis function. The trajectory basis function might be the Discrete Cosine Transform(DCT), Walsh-Hadamard transformation(WHT) or some other transforms. So it needed to determine a good basis function.In view of above problems, this dissertation will launch following parts of works based on existing researches.(1) In order to determine a suitable size number of trajectory basis, this dissertation proposes an algorithm named sparse approximation method. The main thoughts of this algorithm are as follows: when recovering the non-rigid object trajectory curves with trajectory basis, a set of sparse coefficients is used to select the basis which can represent the feature of each curve from the trajectory basis matrix automatically. The sparse coefficients can not only recover the non-rigid object motion trajectory curves as far as possible, but also avoid missing the details of the motion for selecting a small size number of the trajectory basis. And because these coefficients are sparse numbers, it must be solved. It can make the computation problem more easily by representing the coefficients matrix corresponding to the trajectory basis matrix as a sparse matrix. Moreover, the sparse approximation method avoids to define a size number of the trajectory basis artificially when solving the NRSfM problem every time. This dissertation has proved the high-performance of the sparse approximation method and the high accuracy of the reconstruction result through testing this method in solving the NRSfM problem.(2) In order to determine a suitable trajectory basis type, this dissertation proposes to combine different trajectory basis types to construct the atoms dictionary and solves the NRSfM problems with sparse approximation method. Because the motions of non-rigid object are random and complex, it would be not possible to recover all of the motions accurately only with one trajectory basis type. This dissertation integrates different trajectory basis types in one irrelevant over-complete atoms dictionary. And then, sparse approximation method is used to solve the atoms coefficients. This method aims to reconstruct the trajectory curves with most matching trajectory basis in the feature area. It will improve the accuracy in recovering the motion structure and get a better result.