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New Constraints on Data-Closeness and Needle Map Consistency for Shape-from-Shading
December 1999 (vol. 21 no. 12)
pp. 1250-1267

Abstract—This paper makes two contributions to the problem of needle-map recovery using shape-from-shading. First, we provide a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint. This not only improves the data closeness of the recovered needle-map, but also removes the necessity for extensive parameter tuning. Second, we exploit the improved ease of control of the new shape-from-shading process to investigate various types of needle-map consistency constraint. The first set of constraints are based on needle-map smoothness. The second avenue of investigation is to use curvature information to impose topographic constraints. Third, we explore ways in which the needle-map is recovered so as to be consistent with the image gradient field. In each case we explore a variety of robust error measures and consistency weighting schemes that can be used to impose the desired constraints on the recovered needle-map. We provide an experimental assessment of the new shape-from-shading framework on both real world images and synthetic images with known ground truth surface normals. The main conclusion drawn from our analysis is that the data-closeness constraint improves the efficiency of shape-from-shading and that both the topographic and gradient consistency constraints improve the fidelity of the recovered needle-map.

[1] E. Angelopoulou, “Gaussian Curvature from Photometric Scatter Plots,” Proc. IEEE Workshop Photometric Modeling for Computer Vision and Graphics, 1999.
[2] P.N. Belhumeur and D.J. Kriegman, "What is the Set of Images of an Object under all Possible Lighting Conditions?," IEEE Proc. Conf. Computer Vision and Pattern Recognition, 1996.
[3] M. Bichsel and A.P. Pentland, “A Simple Algorithm for Shape from Shading,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 459-465, 1992.
[4] M.J. Brooks and B.K.P. Horn, “Shape and Source from Shading,” Proc. Int'l Joint Conf. Artifical Intelligence, pp. 932-936, 1985.
[5] A.M. Bruckstein, “On Shape from Shading,” Computer Vision, Graphics, and Image Processing, vol. 44, pp. 139-154, 1988.
[6] F.P. Ferrie and J. Lagarde, “Curvature Consistency Improves Local Shading Analysis,” Proc. IEEE Int'l Conf. Pattern Recognition, vol. I, pp. 70-76, 1990.
[7] D. Hilbert and R. Courant, Methods of Math. Physics. 1953.
[8] D.C. Hoaglin, F. Mosteller, and J.W. Tukey, eds., , Understanding Robust and Exploratory Data Analysis. Wiley, New York.: 1983.
[9] B.K.P. Horn, “Obtaining Shape from Shading Information.” The Psychology of Computer Vision, P.H. Winston, ed., McGraw Hill, New York.: pp. 115-155, 1975.
[10] B.K.P. Horn, and M.J. Brooks, “The Variational Approach to Shape from Shading,” Computer Vision, Graphics, and Image Processing, vol. 33. no. 2, pp. 174-208, 1986.
[11] Shape from Shading, B.K.P. Horn and M.J. Brooks, eds. Cambridge, Mass.: MIT Press, 1989.
[12] B.K.P. Horn, “Height and Gradient from Shading,” Proc. Int'l Joint Conf. Artifical Intelligence, vol. 5, no. 1, pp. 37-75, 1990.
[13] P. Huber, Robust Statistics. Chichester: Wiley, 1981.
[14] K. Ikeuchi and B.K.P. Horn, “Numerical Shape from Shading and Occluding Boundaries,” Artificial Intelligence, vol. 17, no. 3, pp. 141-184, 1981.
[15] R. Kimmel and A.M. Bruckstein, “Tracking Level-Sets by Level-Sets: A Method for Solving the Shape from Shading Problem,” Computer Vision and Image Understanding, vol. 62, no. 1, pp. 47-58, 1995.
[16] J.J. Koenderink and A.J. van Doorn, “Surface Shape and Curvature Scales,” Image and Vision Computing, vol. 10, pp. 557-565, 1992.
[17] J.J. Koenderink and A.J. van Doorn, “Relief Pictorial and Otherwise,” Image and Vision Computing, vol. 13, no. 5, pp. 321-334, 1995.
[18] J.J. Koenderink, A.J. van Doorn, C. Christou, and J.S. Lappin, “Perturbation Study of Shading in Pictures,” Perception, vol. 25, no. 9, pp. 1,009-1,026, 1996.
[19] K.M. Lee and C.C.J. Kuo, “Shape from Shading with a Linear Triangular Element Surface Model,” IEEE Pattern Analysis and Machine, vol. 15, no. 8, pp. 815-822, 1993.
[20] S.Z. Li, “Discontinuous MRF Prior and Robust Statistics: A Comparative Study,” Image and Vision Computing, vol. 13, no. 3, pp. 227-233, 1995.
[21] D.C. Marr, Vision. San Francisco, Calif.: Freeman, 1982.
[22] J. Oliensis, “Shape from Shading as a Partially Well-Constrained Problem,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 559-564, 1991.
[23] J. Oliensis and P. Dupuis, “A Global Algorithm for Shape from Shading,” Proc. IEEE Int'l Conf. Computer Vision, pp. 692-701, 1993.
[24] P. Parent and S.W. Zucker, “Curvature Consistency and Curve Detection,” J. Opt. Soc. America A, vol. 2, no. 13, p. 5, 1985.
[25] A.P. Pentland, “Local Shading Analysis,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, pp. 170-187, 1984.
[26] A.P. Pentland, “Finding the Illuminant Direction,” J. Optical Society of America, pp. 448-455, 1982.
[27] T. Poggio, V. Torre, and C. Koch, “Computational Vision and Regularization Theory,” Nature, vol. 317, pp. 314-319, 1985.
[28] P.S. Tsai and M. Shah, “Shape from Shading Using Linear Approximation,” Image and Vision Computing, vol. 12, no. 8, pp. 487-498, 1994.
[29] J.A. Sethian, Level Set Methods. Cambridge Univ. Press 1996.
[30] R. Szeliski, “Fast Shape from Shading,” Computer Vision, Graphics, and Image Processing: Image Understanding, vol. 53, pp. 129-153, 1991.
[31] P.L. Worthington and E.R. Hancock, “Shape-from-Shading using Robust Statistics,” Proc. IEEE Int'l Conf. Digital Signal Processing, 1997.
[32] P.L. Worthington and E.R. Hancock, “Needle Map Recovery Using Robust Regularizers,” Proc. British Machine Vision Conf., BMVA Press, vol. I, pp. 31-40, 1997.
[33] P.L. Worthington and E.R. Hancock, “Needle Map Recovery using Robust Regularizers,” Image and Vision Computing, vol. 17, no. 8, pp. 545-558, 1999.
[34] P.L. Worthington and E.R. Hancock, “Data Driven Shape-from-Shading using Curvature Consistency,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. I, pp. 287-292, 1999.
[35] P.L. Worthington and E.R. Hancock, “3D Surface Topography from Intensity Images,” Proc. IEEE Int'l Conf. Computer Vision, vol. II, pp. 911-917, 1999.
[36] R. Zhang, P.S. Tsai, J.E. Cryer, and M. Shah, "Analysis of Shape From Shading Techniques," Proc. IEEE Computer Society Conf. Computer Vision and Pattern Recognition, pp. 377-384, 1994.
[37] Q. Zheng and R. Chellappa, Estimation of Illuminant Direction, Albedo, and Shape from Shading IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp. 680-702, July 1991.

Index Terms:
Index Terms–Shape-from-shading, hard constraints, curvature consistency, gradient consistency, robust statistics.
Citation:
Philip L. Worthington, Edwin R. Hancock, "New Constraints on Data-Closeness and Needle Map Consistency for Shape-from-Shading," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 12, pp. 1250-1267, Dec. 1999, doi:10.1109/34.817406
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