| The applications of the Matrix recovery and 3D reconstruction is to restore movement structure,from one or several images to recover the target’s 3D information,including the camera motion parameters and the structure of 3D scene,which is one of the hot spots in computer vision.As an important data analysis tool,matrix recovery have many applications in recovering the occluded feature points in the image,taking advantage of the redundant information of image matrix.The thesis studies matrix recovery and its application in 3D reconstruction.Firstly,this thesis introduces the current research situation on the restoration of the occluded points in 3D reconstruction,the camera models and its imaging models,singular value decomposition.Secondly,the thesis discusses matrix recovery and its application in 3D reconstruction.Finally,it mainly studies how to recover the occluded points feature points in the image sequence under the orthographic projection model.The proposed algorithms aim at improving robustness,precision and recovery efficiency for the recovery of the occluded feature points in the image sequence under the orthographic projection model.The main innovation results of this paper are as follows:(1)Based on the matrix recovery theory,the thesis proposes a low rank matrix recovery method based on column constraints and SVD.The experiments with simulated data show that the proposed method has a better recovery rate.And compared with Martinec method,the experiments once again show that the proposed method has the advantages of fast convergence speed and small error.(2)Based on the low rank matrix recovery method based on column constraints and SVD,a low rank matrix recovery method based on row and column constraints and SVD under orthographic projection is presented.Utilizing the property that the dimension of both the row and the column spaces of image matrix are 3,the method replaces occlusion solution by iteratively solving the minimum of quadratic function.Because the quadratic function is convex,and it only needs one step to get the extreme value,this method also has good numerical characteristics.Theoretical demonstration shows that the method can converge to the global optimal solution.And compared with the Wiberg and Noguer methods,experiments show that the proposed method has the advantages of fast convergence speed and small error. |
