一种鲁棒的基于光度立体视觉的表面重建方法

吴仑; 王涌天; 刘越

doi:10.3724/SP.J.1004.2013.01339

一种鲁棒的基于光度立体视觉的表面重建方法

doi: 10.3724/SP.J.1004.2013.01339

1.
北京理工大学光电学院北京 100086

基金项目:

国家重点基础研究发展计划(973计划) (2010CB732505);国家自然科学基金(61072096)资助

详细信息

作者简介:
吴仑北京理工大学光电学院博士研究生. 2006 年获北京理工大学光学工程专业硕士学位. 主要研究方向为运动结构重建与数学优化方法.E-mail: lun.wu@hotmail.com

计量
- 文章访问数: 2127
- HTML全文浏览量: 78
- PDF下载量: 1377
- 被引次数: 0
出版历程
- 收稿日期: 2011-12-12
- 修回日期: 2012-07-15
- 刊出日期: 2013-08-20

A Robust Approach Based on Photometric Stereo for Surface Reconstruction

1.
School of Optoelectronics, Beijing Institute of Technology, Beijing 100086

Funds:

Supported by National Basic Research Program of China (973 program) (2010CB732505) and National Natural Science Foundation of China (61072096)

摘要

摘要: 提出一种基于先进的凸优化技术的光度立体视觉重建框架. 首先通过鲁棒的主成分分析(Robust principle component analysis, RPCA)祛除图像噪声, 得到低秩矩阵和物体表面向量场, 然后再通过表面重建算法从向量场来恢复物体形状. 相对于先前的一些使用最小二乘或者一些启发式鲁棒技术的方法, 该方法使用了所有可用的信息, 可以同时修复数据中的丢失和噪声数据, 显示出了较高的计算效率以及对于大的稀疏噪声的鲁棒性. 实验结果表明, 本文提出的框架大大提高了在噪声存在情况下物体表面的重建精度.
- 光度立体视觉 /
- 鲁棒主成分分析 /
- 表面重建 /
- 稀疏噪声 /
- 低秩矩阵
Abstract: We present a new framework for surface reconstruction with technique of photometric stereo, which is based on advanced convex optimization technique. We firstly remove the errors in images by robust principle component analysis (RPCA), and then obtain low-rank matrix and surface normal field. Unlike previous approaches, this method uses all the available information to simultaneously fix missing and erroneous entries. The new technique is more computationally efficient and provides theoretical assurance for robustness to large errors. Experimental results demonstrate that this framework can improve the precision for surface reconstruction with noise.
- Photometric stereo /
- robust principle component analysis (RPCA) /
- surface reconstruction /
- sparse error /
- low-rank matrix

HTML全文

参考文献(30)

[1]	Woodham R J. Photometric method for determining surface orientation from multiple images. Optical Engineering, 1980, 19(1): 139-144
[2]	Shashua A. Geometry and Photometry in 3D Visual Recognition[Ph.D. dissertation], Massachusetts Institute of Technology Cambridge, USA, 1992
[3]	Belhumeur P N, Kriegman D J. What is the set of images of an object under all possible lighting conditions? In: Proceedings of the 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. San Francisco, USA: IEEE, 1996. 270-227
[4]	Basri R, Jacobs D W. Lambertian reflectance and linear subspaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(2): 218-233
[5]	Georghiades A S, Kriegman D J, Belhumeur P N. From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(6): 643-660
[6]	Hayakawa H. Photometric stereo under a light source with arbitrary motion. Journal of the Optical Society of America, 1994, 11(11): 3079-3089
[7]	Jolliffe I T. Principal Component Analysis. New York: Springer-Verlag, 1986
[8]	Belhumeur P N, Kriegman D J, Yuille A L. The bas-relief ambiguity. In: Proceedings of the 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. San Juan, Puerto Rico: IEEE, 1997. 1060-1066
[9]	Shi B X, Matsushita Y, Wei Y C, Xu C, Tan P. Self-calibrating photometric stereo. In: Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. San Francisco, USA: IEEE, 2010. 1118-1125
[10]	Jacobs D. Linear fitting with missing data: applications to structure-from-motion and to characterizing intensity images. In: Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition. San Juan, Puerto Rico: IEEE, 1997. 206-212
[11]	Yuille A L, Snow D, Epstein R, Belhumeur P N. Determining generative models of objects under varying illumination: shape and albedo from multiple images using SVD and integrability. International Journal of Computer Vision, 1999, 35(3): 203-222
[12]	Fischler M A, Bolles R C. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 1981, 24(6): 381-395
[13]	Juliá C, Lumbreras F, Sappa A D. A factorization-based approach to photometric stereo. International Journal of Imaging Systems and Technology, 2011, 21(1): 115-119
[14]	Guerreiro R F C, Aguiar P M Q. Estimation of rank deficient matrices from partial observations: two-step iterative algorithms. EMMCVPR. Lisbon, Portugal: Springer, 2003. 450-466
[15]	Chen P. Optimization algorithms on subspaces: revisiting missing data problem in low-rank matrix. International Journal of Computer Vision, 2008, 80(1): 125-142
[16]	Mukaigawa Y, Ishii Y, Shakunaga T. Analysis of photometric factors based on photometric linearization. Journal of the Optical Society of America, 2007, 24(10): 3326-3334
[17]	Miyazaki D, Hara K, Ikeuchi K. Median photometric stereo as applied to the segonko tumulus and museum objects. International Journal of Computer Vision, 2010, 86(2-3): 229-242
[18]	Candés E, Li X D, Ma Y, Wright J. Robust principal component analysis? Journal of the ACM, 2011, 58(3): 1-37
[19]	Wu L, Ganesh A, Shi B X, Matsushita Y, Wang Y T, Ma Y. Robust photometric stereo via low-rank matrix completion and recovery. In: Proceedings of the 10th Asian Conference on Computer Vision. Queenstown New Zealand: Springer, 2010. 703-717
[20]	Simchony T, Chellappa R, Shao M. Direct analytical methods for solving Possion equations in computer vision problems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, 12(5): 435-446
[21]	Chandrasekaran V, Sanghavi S, Parrilo P A, Willsky A S. Sparse and low-rank matrix decompositions. In: Proceedings of the 47th Annual Allerton Conference on Communication, Control, and Computing. Monticello, IL: IEEE, 2009. 962-967
[22]	Lin Z C, Chen M M, Wu L Q, Ma Y. The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-rank Matrices. Technical Report UILU-ENG-09-2215, UIUC, USA, 2009
[23]	Recht B, Fazel M, Parillo P A. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Review, 2010, 52(3): 471-501
[24]	Candés E, Recht B. Exact matrix completion via convex optimization. Foundation of Computational Mathematics, 2008, 9(6): 717-772
[25]	Candés E, Tao T. The power of convex relaxation: near-optimal matrix completion. IEEE Transactions on Information Theory, 2010, 56(5): 2053-2080
[26]	Ganesh A, Lin Z C, Wright J, Wu L Q, Chen M M, Ma Y. Fast algorithms for recovering a corrupted low-rank matrix. In: Proceedings of the 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing. Aruba, Dutch Antilles: IEEE, 2009. 213-216
[27]	Toh K C, Yun S. An accelerated proximal gradient algorithm for nuclear norm regularized least squares problems. Pacific Journal of Optimization, 2010, 6: 615-640
[28]	Bertsekas D P. Nonlinear Programming. Belmont, MA: Athena Scientific, 2004
[29]	Cook R L, Torrance K E. A reflectance model for computer graphics. ACM SIGGRAPH Computer Graphics, 1981, 15(3): 307-316
[30]	Zhou Z H, Li X D, Wright J, Candés E, Ma Y. Stable principal component pursuit. In: Proceedings of the 2010 IEEE International Symposium on Information Theory. Austin, USA: IEEE, 2010. 1518-1522