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Issue No.02 - February (2011 vol.33)
pp: 419-426
Carlos Hernández , Google Inc., Seattle
George Vogiatzis , Aston University, Birmingham
Roberto Cipolla , University of Cambridge, Cambridge
Light occlusions are one of the most significant difficulties of photometric stereo methods. When three or more images are available without occlusion, the local surface orientation is overdetermined so that shape can be computed and the shadowed pixels can be discarded. In this paper, we look at the challenging case when only two images are available without occlusion, leading to a one degree of freedom ambiguity per pixel in the local orientation. We show that, in the presence of noise, integrability alone cannot resolve this ambiguity and reconstruct the geometry in the shadowed regions. As the problem is ill-posed in the presence of noise, we describe two regularization schemes that improve the numerical performance of the algorithm while preserving the data. Finally, the paper describes how this theory applies in the framework of color photometric stereo where one is restricted to only three images and light occlusions are common. Experiments on synthetic and real image sequences are presented.
Photometric stereo, shadows.
Carlos Hernández, George Vogiatzis, Roberto Cipolla, "Overcoming Shadows in 3-Source Photometric Stereo", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.33, no. 2, pp. 419-426, February 2011, doi:10.1109/TPAMI.2010.181
[1] S. Barsky and M. Petrou, "The 4-Source Photometric Stereo Technique for Three-Dimensional Surfaces in the Presence of Highlights and Shadows" IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 10 pp. 1239-1252, Oct. 2003.
[2] M. Chandraker, S. Agarwal, and D. Kriegman, "Shadowcuts: Photometric Stereo with Shadows," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2007.
[3] M. Drew, "Reduction of Rank-Reduced Orientation-from-Color Problem with Many Unknown Lights to Two-Image Known-Illuminant Photometric Stereo," Proc. IEEE Int'l Symp. Computer Vision, pp. 419-424, 1995.
[4] A. Petrov, "Light, Color and Shape," Cognitive Processes and Their Simulation (in Russian), pp. 350-358, 1987.
[5] C. Hernández, G. Vogiatzis, G. Brostow, B. Stenger, and R. Cipolla, "Non-Rigid Photometric Stereo with Colored Lights," Proc. 11th Int'l Conf. Computer Vision (ICCV), 2007.
[6] C. Hernández, G. Vogiatzis, R. Cipolla, "Shadows in Three-Source Photometric Stereo," Proc. 10th European Conf. Computer Vision, 2008.
[7] R. Woodham, "Photometric Method for Determining Surface Orientation from Multiple Images," Optical Eng., vol. 19, pp. 139-144, 1980.
[8] S. Lee and M. Brady, "Integrating Stereo and Photometric Stereo to Monitor the Development of Glaucoma," Image and Vision Computing, vol. 9, pp. 39-44, 1991.
[9] R. Onn and A. Bruckstein, "Integrability Disambiguates Surface Recovery in Two-Image Photometric Stereo," Int'l J. Computer Vision, vol. 5, pp. 105-113, 1990.
[10] E.N. Coleman,Jr., and R. Jain, "Obtaining 3-Dimensional Shape of Textured and Specular Surfaces Using Four-Source Photometry," Shape Recovery, pp. 180-199, Jones and Bartlett Publishers Inc., 1992.
[11] A. Yuille and D. Snow, "Shape and Albedo from Multiple Images Using Integrability," Proc. Conf. Computer Vision and Pattern Recognition, p. 158, 1997.,
[12] M. Daum and G. Dudek, "On 3-D Surface Reconstruction Using Shape from Shadows," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, p. 461, 1998.
[13] Y. Yu and J.T. Chang, "Shadow Graphs and Third Texture Reconstruction," Int'l J. Computer Vision, vol. 62, pp. 35-60, 2005.
[14] A. Tankus and N. Kiryati, "Photometric Stereo under Perspective Projection," Proc. 10th Int'l Conf. Computer Vision, pp. 611-616, 2005.
[15] L.B. Wolff and E. Angelopoulou, "Third Stereo Using Photometric Ratios," Proc. Third European Conf. Computer Vision (Vol. II), pp. 247-258, 1994.
[16] J. Fan and L.B. Wolff, "Surface Curvature and Shape Reconstruction from Unknown Multiple Illumination and Integrability," Computer Vision and Image Understanding, vol. 65, pp. 347-359, 1997.
[17] H. Chen, P. Belhumeur, and D. Jacobs, "In Search of Illumination Invariants," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 254-261, 2000.
[18] T.A. Davis, "Algorithm 832: Umfpack, an Unsymmetric-Pattern Multifrontal Method," ACM Trans. Math. Software, vol. 30, pp. 196-199, 2004.
[19] K. Ikeuchi and B. Horn, "Numerical Shape from Shading and Occluding Boundaries," Artificial Intelligence, vol. 17, pp. 141-184, 1981.
[20] M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, "Image Inpainting," Proc. ACM SIGGRAPH '00, pp. 417-424, 2000.
[21] A. Agrawal, R. Raskar, and R. Chellappa, "What Is the Range of Surface Reconstructions from a Gradient Field?," Proc. Ninth European Conf. Computer Vision, pp. 578-591, 2006.
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