基于l_1范数最小化的非流形曲线族重构  

Non-Manifold Curve Reconstruction Based on l_1 Minimization

作　　者：骆沛[1] 吴壮志[1] 夏春和[1] 马腾[1] 

机构地区：[1]北京航空航天大学计算机学院,北京100191

出　　处：《计算机学报》2013年第9期1917-1928,共12页Chinese Journal of Computers

摘　　要：从散乱点集重构曲线族在计算机视觉、逆向工程和医学图像处理等方面有着广泛的应用,非流形曲线族重构是其中的难点问题.文中在压缩传感理论基础上,提出一种基于l1范数最小化的非流形曲线族重构方法.该方法首先将散乱点集的法矢和位置信号表示为稀疏形式,通过l1范数优化方法,重建法矢信号和位置信号;之后,根据重建的法矢和位置计算点集的双边权,在此基础上构建最小生成树(Minimum Spanning Tree,MST)来重构曲线族;最后通过后处理过程,完成对重构曲线族的开闭处理.实验表明,该算法能处理包含开、闭曲线,流形、非流形曲线,以及具有尖锐特征的曲线等复杂情况的曲线族,并且对噪声较鲁棒.Curve reconstruction from unorganized computer vision, reverse engineering and medical curve reconstruction is a difficult problem. In this posed for non-manifold curve reconstruction based points is widely used in various fields such as image processing, among which non-manifold paper, an e1 norm minimization method is proon compressive sensing theory. First, we give the sparse representation of the points normals and locations, and restore them via e1 norm optimization. Then, the restored normals and positions are used to calculate the bilateral weights and build a minimum spanning tree on them. Finally, post-processing is performed to manage the open and close states of the curves. Experiments show that the algorithm is robust to noise and can handle complex family of curves which contains open/closed curves, manifold/non-manifold curves and curves with sharp features.

关 键 词：非流形曲线 压缩传感 e1范数最小化 曲线重构 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]