Shape From Shading

Shape From Shading is the process of computing the three-dimensional shape of a surface from one image of that surface. Contrary to most of the other three-dimensional reconstruction problems (for example, stereo and photometric stereo), in the Shape From Shading problem, data are minimal (we use a single image!). As a consequence, this inverse problem is intrinsically a difficult one. In this chapter we describe the main difficulties of the problem and the most recent theoretical results. We also give some examples of realistic modeling and of rigorous numerical methods.

[1]  E. Rouy,et al.  A viscosity solutions approach to shape-from-shading , 1992 .

[2]  Wojciech Chojnacki,et al.  Shading without shape , 1992 .

[3]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[4]  G. Barles,et al.  Convergence of approximation schemes for fully nonlinear second order equations , 1990, 29th IEEE Conference on Decision and Control.

[5]  Reinhard Klette,et al.  Shape from Shading and Photometric Stereo Methods , 1998 .

[6]  Alfred M. Bruckstein,et al.  Shape from Shading , 2020, Computer Vision.

[7]  C.-C. Jay Kuo,et al.  Shape from Shading with a Generalized Reflectance Map Model , 1997, Comput. Vis. Image Underst..

[8]  John Oliensis,et al.  Uniqueness in shape from shading , 1991, International Journal of Computer Vision.

[9]  Edwin R. Hancock,et al.  A probabilistic framework for specular shape-from-shading , 2002, Object recognition supported by user interaction for service robots.

[10]  Berthold K. P. Horn.  Obtaining shape from shading information , 1989 .

[11]  Olivier Faugeras,et al.  A viscosity method for Shape-from-Shading without boundary data , 2004 .

[12]  Hideo Saito,et al.  A divide-and-conquer strategy in shape from shading problem , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[13]  Jean-Denis Durou,et al.  A Survey of Numerical Methods for Shape from Shading , 2004 .

[14]  Olivier D. Faugeras,et al.  "Perspective shape from shading" and viscosity solutions , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[15]  Tsnsliiiiia Nala,et al.  Shape from Shading with Interreflections under Proximal Light Source - 3D shape Reconstruction of Unfolded Book Surface from a Scanner Image - , 1995 .

[16]  Anna R. Bruss.  The Eikonal equation: some results applicable to computer vision , 1982 .

[17]  Ryszard Kozera,et al.  Uniqueness in Shape from Shading Revisited , 1997, Journal of Mathematical Imaging and Vision.

[18]  G. Barles.  Solutions de viscosité des équations de Hamilton-Jacobi , 1994 .

[19]  Fabio Camilli,et al.  An approximation scheme for the maximal solution of the shape-from-shading model , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[20]  Olivier D. Faugeras,et al.  Shape from Shading and Viscosity Solutions , 2002, ECCV.

[21]  Yehezkel Yeshurun,et al.  Reconstruction of medical images by perspective shape-from-shading , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[22]  Olivier D. Faugeras,et al.  Unifying Approaches and Removing Unrealistic Assumptions in Shape from Shading: Mathematics Can Help , 2004, ECCV.

[23]  Jean-Denis Durou,et al.  Ambiguous Shape from Shading with Critical Points , 2004, Journal of Mathematical Imaging and Vision.

[24]  J. Oliensis,et al.  Shape from shading as a partially well-constrained problem , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[25]  Michael J. Brooks.  Two Results Concerning Ambiguity in Shape From Shading , 1983, AAAI.

[26]  Alex Pentland,et al.  Local Shading Analysis , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  Yee-Hong Yang,et al.  Shape from shading for non-Lambertian surfaces , 1994, Proceedings of 1st International Conference on Image Processing.

[28]  P. Dupuis,et al.  An Optimal Control Formulation and Related Numerical Methods for a Problem in Shape Reconstruction , 1994 .

[29]  Alfred M. Bruckstein,et al.  Tracking Level Sets by Level Sets: A Method for Solving the Shape from Shading Problem , 1995, Comput. Vis. Image Underst..

[30]  Qiang Ji,et al.  Digital imaging colposcopy: corrected area measurements using shape-from-shading , 1998, IEEE Transactions on Medical Imaging.

[31]  Pierre Gurdjos,et al.  Towards shape from shading under realistic photographic conditions , 2004, ICPR 2004.

[32]  Olivier Faugeras,et al.  A mathematical and algorithmic study of the Lambertian SFS problem for orthographic and pinhole cameras , 2003 .

[33]  David J. Kriegman,et al.  The Bas-Relief Ambiguity , 2004, International Journal of Computer Vision.

[34]  P. Souganidis,et al.  Differential Games and Representation Formulas for Solutions of Hamilton-Jacobi-Isaacs Equations. , 1983 .

[35]  Yehezkel Yeshurun,et al.  A new perspective [on] shape-from-shading , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[36]  Alexander Vladimirsky,et al.  Ordered Upwind Methods for Static Hamilton-Jacobi Equations: Theory and Algorithms , 2003, SIAM J. Numer. Anal..

[37]  P. Lions,et al.  Shape-from-shading, viscosity solutions and edges , 1993 .

[38]  Alper Yilmaz,et al.  Level Set Methods , 2007, Wiley Encyclopedia of Computer Science and Engineering.

[39]  P. Danielsson.  Euclidean distance mapping , 1980 .

[40]  Ron Kimmel,et al.  Optimal Algorithm for Shape from Shading and Path Planning , 2001, Journal of Mathematical Imaging and Vision.