On Differential Photometric Reconstruction for Unknown, Isotropic BRDFs

被引:47
作者
Chandraker, Manmohan [1 ]
Bai, Jiamin [2 ]
Ramamoorthi, Ravi [2 ]
机构
[1] NEC Labs Amer Inc, Cupertino, CA 95014 USA
[2] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA
关键词
Surface reconstruction; general BRDF; photometric invariants; differential theory; SHAPE; STEREO;
D O I
10.1109/TPAMI.2012.217
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This paper presents a comprehensive theory of photometric surface reconstruction from image derivatives in the presence of a general, unknown isotropic BRDF. We derive precise topological classes up to which the surface may be determined and specify exact priors for a full geometric reconstruction. These results are the culmination of a series of fundamental observations. First, we exploit the linearity of chain rule differentiation to discover photometric invariants that relate image derivatives to the surface geometry, regardless of the form of isotropic BRDF. For the problem of shape-from-shading, we show that a reconstruction may be performed up to isocontours of constant magnitude of the gradient. For the problem of photometric stereo, we show that just two measurements of spatial and temporal image derivatives, from unknown light directions on a circle, suffice to recover surface information from the photometric invariant. Surprisingly, the form of the invariant bears a striking resemblance to optical flow; however, it does not suffer from the aperture problem. This photometric flow is shown to determine the surface up to isocontours of constant magnitude of the surface gradient, as well as isocontours of constant depth. Further, we prove that specification of the surface normal at a single point completely determines the surface depth from these isocontours. In addition, we propose practical algorithms that require additional initial or boundary information, but recover depth from lower order derivatives. Our theoretical results are illustrated with several examples on synthetic and real data.
引用
收藏
页码:2941 / 2955
页数:15
相关论文
共 23 条
[1]  
Alldrin N., 2007, P IEEE INT C COMP VI
[2]  
[Anonymous], 2010, CVX: Matlab software for disciplined convex programming (web page and software)
[3]  
[Anonymous], 1976, Differential Geometry of Curves and Surfaces
[4]  
[Anonymous], 2008, P IEEE C COMP VIS PA
[5]   The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows [J].
Barsky, S ;
Petrou, M .
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2003, 25 (10) :1239-1252
[6]  
Brooks M. J., 1985, P INT JOINT C ART IN
[7]  
Chandraker M., 2011, 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), P2505, DOI 10.1109/CVPR.2011.5995603
[8]  
Clark J. J., 1992, Proceedings. 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.92CH3168-2), P29, DOI 10.1109/CVPR.1992.223231
[9]   Example-based photometric stereo: Shape reconstruction with general, varying BRDFs [J].
Hertzmann, A ;
Seitz, SM .
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2005, 27 (08) :1254-1264
[10]   Consensus Photometric Stereo [J].
Higo, Tomoaki ;
Matsushita, Yasuyuki ;
Ikeuchi, Katsushi .
2010 IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR), 2010, :1157-1164