矩阵恢复及其在三维重建中的应用

【作者】 张力；

【导师】 裘国永；

【作者基本信息】 陕西师范大学 ， 计算机软件与理论， 2017， 硕士

【摘要】 三维重建中的运动恢复结构,是从一个或若干图像中恢复出目标物的三维信息,其中包括摄像机的运动参数和三维场景的结构信息,这是计算机视觉领域的重要问题。矩阵恢复作为本领域的一种重要的数据分析工具,在利用图像矩阵的冗余信息恢复图像遮挡的特征点等方面有很多应用。本文认真分析了国内外研究现状,对矩阵恢复方法及其在三维重建中的应用进行了探讨。首先介绍了三维重建中遮挡点的恢复研究现状,对本文所涉及的相机模型及其成像模型、奇异值分解(SVD分解)等进行了详述。其次,介绍矩阵恢复及其在三维重建中的应用。最后,重点研究了在正投影模型下实现对图像序列的遮挡点恢复。本论文提出的算法目的在于改进图像遮挡点恢复算法的鲁棒性、精度和效率。本文的主要创新工作如下:(1)基于矩阵恢复理论,提出了一种基于奇异值分解和列约束的低秩矩阵恢复方法。仿真实验结果表明,本文提出的方法具有较好的恢复效率。并与Martinec方法作对比实验,证明本文方法有较好的收敛速度和恢复效果。(2)在基于列约束的低秩矩阵恢复方法基础之上,又提出了一种基于奇异值分解和行列约束的低秩矩阵恢复方法。该方法利用奇异值分解及图像矩阵的行空间和列空间都是三维的特性,将遮挡点的求解转化为一个二次型的迭代求解。由于二次型具有良好的数值求解特性,如函数为凸函数、一步就可以求解出函数的极值等,因而此方法也具有良好的数值求解特性,从理论上证明了算法的收敛性。与Wiberg方法和Noguer方法所做的对比实验表明,本文算法具有更高的收敛速度和恢复效果。更多还原

【Abstract】 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.更多还原