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Dense Mirroring Surface Recovery from 1D Homographies and Sparse Correspondences
February 2011 (vol. 33 no. 2)
pp. 325-337
Stas Rozenfeld, Technion, Israel Institute of Technology, Haifa
Ilan Shimshoni, University of Haifa, Haifa
Michael Lindenbaum, Technion, Israel Institute of Technology, Haifa
In this work, we recover the 3D shape of mirrors, sunglasses, and stainless steel implements. A computer monitor displays several images of parallel stripes, each image at a different angle. Reflections of these stripes in a mirroring surface are captured by the camera. For every image point, the direction of the displayed stripes and their reflections in the image are related by a 1D homography matrix, computed with a robust version of the statistically accurate heteroscedastic approach. By focusing on a sparse set of image points for which monitor-image correspondence is computed, the depth and the local shape may be estimated from these homographies. The depth estimation relies on statistically correct minimization and provides accurate, reliable results. Even for the image points where the depth estimation process is inherently unstable, we are able to characterize this instability and develop an algorithm to detect and correct it. After correcting the instability, dense surface recovery of mirroring objects is performed using constrained interpolation, which does not simply interpolate the surface depth values but also uses the locally computed 1D homographies to solve for the depth, the correspondence, and the local surface shape. The method was implemented and the shape of several objects was densely recovered at submillimeter accuracy.

[1] Y. Adato, Y. Vasilyev, O. Ben-Shahar, and T. Zickler, "Toward a Theory of Shape from Specular Flow," Proc. IEEE Int'l Conf. Computer Vision, pp. 1-8, 2007.
[2] M. Baba, K. Ohtani, M. Imai, and T. Konishi, "New Laser Rangefinder for Three-Dimensional Shape Measurement of Specular Objects," Optical Eng., vol. 40, no. 1, pp. 53-60, 2001.
[3] A. Blake and G. Brelstaff, "Geometry from Specularities," Proc. IEEE Int'l Conf. Computer Vision, pp. 394-403, 1988.
[4] T. Bonfort and P. Sturm, "Voxel Carving for Specular Surfaces," Proc. IEEE Int'l Conf. Computer Vision, pp. 591-596, 2003.
[5] M. Halstead, B. Barsky, S. Klein, and R. Mandell, "Reconstructing Curved Surfaces from Specular Reflection Patterns Using Spline Surfce Fitting of Normals," Proc. ACM Conf. Computer Graphics and Interactive Techniques, pp. 335-342, 1996.
[6] M.C. Knauer, J. Kaminski, and G. Häusler, "Phase Measuring Deflectometry: A New Approach to Measure Specular Free-Form Surfaces," Optical Metrology in Production Eng., W. Osten and M. Takeda, eds., pp. 366-376, SPIE, 2004.
[7] Y. Leedan and P. Meer, "Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint," Int'l J. Computer Vision, vol. 37, no. 2, pp. 127-150, June 2000.
[8] J. Lellmann, J. Balzer, A. Rieder, and J. Beyerer, "Shape from Specular Reflection and Optical Flow," Int'l J. Computer Vision, vol. 80, no. 2, pp. 226-241, Nov. 2008.
[9] R. Morano, C. Ozturk, R. Conn, S. Dubin, S. Zietz, and J. Nissanov, "Structured Light Using Pseudorandom Codes," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 3, pp. 322-327, Mar. 1998.
[10] M. Oren and S. Nayar, "A Theory of Specular Surface Geometry," Proc. IEEE Int'l Conf. Computer Vision, pp. 740-747, 1995.
[11] W. Park and H. Cho, "Measurement of the 3-Dimensional Shapes of Specular Objects Using Recursive Triangulation," Proc. Pacific Conf. Manufacturing, vol. 1, pp. 389-394, 1996.
[12] W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C. Cambridge Univ. Press, 1988.
[13] A. Ripsman and M. Jenkin, "Local Surface Reconstruction of Objects in Space," Proc. IEEE Int'l Symp. Computational Intelligence, 2001.
[14] S. Roth and M. Black, "Specular Flow and the Recovery of Surface Structure," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1869-1876, 2006.
[15] S. Rozenfeld, I. Shimshoni, and M. Lindenbaum, "Dense Mirroring Surface Recovery from 1D Homographies and Sparse Correspondences," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1-8, 2007.
[16] S. Savarese, M. Chen, and P. Perona, "Local Shape from Mirror Reflections," Int'l J. Computer Vision, vol. 64, no. 1, pp. 31-67, Aug. 2005.
[17] J. Solem, H. Aanaes, and A. Heyden, "Variational Surface Interpolation from Sparse Point and Normal Data," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 1, pp. 181-184, Jan. 2007.
[18] M. Tarini, H.P.A. Lensch, M. Goesele, and H.-P. Seidel, "3D Acquisition of Mirroring Objects Using Striped Patterns," Graphical Models, vol. 67, no. 4, pp. 233-259, 2005.
[19] J. Zheng and A. Murata, "Acquiring a Complete 3D Model from Specular Motion under the Illumination of Circular-Shaped Light Sources," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 8, pp. 913-920, Aug. 2000.
[20] A. Zisserman, P.J. Giblin, and A. Blake, "The Information Available to a Moving Observer from Specularities," Image and Vision Computing, vol. 7, no. 1, pp. 38-42, 1989.

Index Terms:
Mirroring objects, 3D shape reconstruction, 1D homographies, stability.
Citation:
Stas Rozenfeld, Ilan Shimshoni, Michael Lindenbaum, "Dense Mirroring Surface Recovery from 1D Homographies and Sparse Correspondences," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 33, no. 2, pp. 325-337, Feb. 2011, doi:10.1109/TPAMI.2010.76
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