This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Recovery of SHGCs From a Single Intensity View
February 1996 (vol. 18 no. 2)
pp. 161-180

Abstract—Generalized Cylinders are a flexible, loosely-defined class of parametric shapes capable of modeling many real-world objects. Straight Homogeneous Generalized Cylinders are an important subclass of Generalized Cylinders, whose cross-sections are scaled versions of a reference curve. Although there has been considerable research into recovering the shape of SHGCs from their contour, this work has almost exclusively involved methods that couple contour and heuristic constraints. A rigorous approach to the problem of recovering solid parametric shape from a single intensity view should involve at least two stages: 1) deriving the contour constraints, and 2) determining if additional image constraints, e.g., intensity, can be used to uniquely determine the 3D object shape. In this paper, the authors follow the approach just described. This methodology is also important for the recovery of object classes like tubes, where contour and heuristic constraints are shown to be insufficient for shape recovery. First, we prove that SHGC contours generated under orthography have exactly two degrees of freedom. Next, we show that the remaining free parameters can be resolved using reflectance-based constraints, without knowledge of the number of light sources, their positions, intensities, the amount of ambient light, or the surface albedo. Finally, the reflectance-based recovery algorithm is demonstrated on both synthetic and real SHGC images.

[1] M. Asada, "Cylindrical shape from contour and shading without knowledge of lighting conditions or surface albedo," Proc. First ICCV, pp. 412-416, June 1987.
[2] M. Asada, T. Nakamura, and Y. Shirai, "Weak Lambertian assumption for determining cylindrical shape and pose from shading and contour," Proc. 1992 CVPR.
[3] M. Asada, T. Nakamura, and Y. Shirai, "A qualitative approach to quantitative recovery of SHGC's shape and pose from shading and contour," Proc. CVPR, 1993.
[4] T.O. Binford, "Visual perception by computer," Proc. IEEE Conf. Systems and Control,Miami, Dec. 1971.
[5] J.M. Brady and A. Yuille, "An extremum principle for shape from contour," MIT, AI Lab, MIT-AIM 711, 1983.
[6] J.M. Brady, J. Ponce, A. Yuille, and H. Asada, "Describing surfaces," Proc. Second Int'l Symp. Robotics Research, Harasuja and Inoue, eds. Cambridge, Mass.: MIT Press, 1985.
[7] R.A. Brooks, "Symbolic reasoning among 3-D models and 2-D images," Artificial Intelligence, vol. 17, pp. 285-348, 1981.
[8] B.-T. Phong, "Illumination for Computer Generated Pictures," Comm. ACM, vol. 18, no. 6, 1975, pp. 311-317.
[9] D.M. Chelberg, "An approach to geometric modeling using generalized cylinders and interpretation of range images using Bayesian networks," PhD thesis, Stanford Univ., 1989.
[10] M.P. Do Carmo, Differential Geometry of Curves and Surfaces.Englewood Cliffs, N.J.: Prentice Hall, 1976.
[11] A.D. Gross and T.E. Boult,“Error of fit for recovering parametric solids,” Second Int’l Conf. Computer Vision, pp. 690-694,Tampa, Fla., 1988.
[12] A.D. Gross and T.E. Boult, "Recovery of straight homogeneous generalized cylinders using contour and intensity information," 1989 SPIE Proc. Visual Comm. and Image Processing IV, pp. 1,661-1,669.
[13] A.D. Gross and T.E. Boult, "An algorithm to recover generalized cylinders from a single intensity view," Proc. IEEE CS 1990 Int'l Conf. Robotics and Automation, pp. 790-795,Cincinnati, Ohio, May 1990.
[14] A.D. Gross, "Toward object-based heuristics," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 8, pp. 794-802, Aug. 1994.
[15] A. Gross, "Analyzing generalized tubular surfaces," Proc. SPIE Conf. Intelligent Robots and Computer Vision,Boston, Nov. 1994.
[16] R. Horaud and J.M. Brady, "On the geometric interpretation of image contours," Proc. First ICCV,London, June 1987.
[17] B.K.P. Horn, "Shape from shading: A method for obtaining the shape of a smooth opaque object from one view," PhD thesis, Dept. of Electrical Eng., MIT, 1970.
[18] B.K.P. Horn, "Hill shading and reflectance map," Proc. IEEE, vol. 69, no. 1, pp. 14-47, Jan. 1981.
[19] K. Ikeuchi and B.K.P. Horn, "Numerical shape from shading and occluding boundaries," Artificial Intelligence, vol. 17, pp. 141-184, 1981.
[20] J. Koënderink, Solid Shape. Cambridge, Mass.: MIT Press, 1991.
[21] J.M. LaVest, R. Glachet, M. Dhome, and J.T. LaPreste, "Modeling solids of revolution by monocular vision," Proc. 1991 CVPR, pp. 690-691,Lahaina, Hawaii, June2-6, 1991.
[22] C.H. Lee and A. Rosenfeld, "Improved methods of estimating shape from shading using the light source coordinate system," Shape from Shading, B.K.P. Horn and M.J. Brooks, eds., pp. 323-369.Cambridge, Mass.: MIT Press, 1989.
[23] D. Marr, "Analysis of occluding contour," Proc. Royal Soc. London, B-197, pp. 441-475, 1977.
[24] S.K. Nayar, K. Ikeuchi, and T. Kanade, "Surface Reflection: Physical and Geometrical Perspectives," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp. 611-634, 1991.
[25] M. Oren and S.K. Nayar, "Generalization of the Lambertian model and implications for machine vision," Technical Report CUCS-057-92, Dept. of Computer Science, Columbia Univ., 1992.
[26] A.P. Pentland, "Local shading analysis," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 3, pp. 170-187, Mar. 1994.
[27] J. Ponce, D. Chelberg, and W. Mann, "Invariant properties of the projections of straight homogeneous generalized cylinders," Proc. First ICCV,London, June 1987.
[28] J. Ponce, "Straight homogeneous generalized cylinders: Differential geometry and uniqueness results," Proc. CVPR, pp. 327-334, June 1988.
[29] J. Ponce, D. Chelberg, and W.B. Mann, "Invariant Properties of Straight Homogeneous Generalized Cylinders and Their Contours," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 9, pp. 951-966, Sept. 1989.
[30] V.S. Ramachandran, "Perceiving shape from shading," Scientific American, vol. 256, no. 2, pp. 58-65, Aug. 1988.
[31] K. Rao and R. Nevatia, "Generalized cone descriptions from sparse 3D data," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 256-263, 1986.
[32] M. Richetin, M. Dhome, and J.T. LaPreste, "Inverse perspective transform from zero-curvature curve points: Application to the localization of some generalized cylinders," Proc. 1989 CVPR,San Diego, June4-8, 1989.
[33] S. Shafer, "The theory of straight homogeneous generalized cylinders," Technical Report CS-083-105, Carnegie Mellon Univ., 1983.
[34] H. Singh and R. Cellappa, "An improved shape from shading algorithm," Technical Report CAR-TR-700, Center for Automated Research, Feb. 1994.
[35] F. Ulupinar and R. Nevatia, "Using symmetries for analysis of shape from contour," Proc. Second ICCV, pp. 414-426, Dec.5-8, 1988.
[36] F. Ulupinar and R. Nevatia, "Shape From Contour: Straight Homogeneous Generalized Cylinders and Constant Cross Section Generalized Cylinders," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 2, pp. 120-135, Feb. 1995.
[37] M. Zerroug and R. Nevatia, "Quasi-invariant properties and 3D shape recovery of non-straight, non-constant generalized cylinders," Proc. DARPA Image Understanding Workshop, pp. 725-735,Washington, D.C., Apr.18-21, 1993.
[38] M. Zerroug and R. Nevatia, "Scene segmentation and volumetric description of SHGCs from a single intensity image," Proc. DARPA Image Understanding Workshop, pp. 905-916,Washington, D.C., Apr.18-21, 1993.
[39] 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:
Computer vision, shape recovery, generalized cylinders, shape from shading, shape from contour.
Citation:
Ari D. Gross, Terrance E. Boult, "Recovery of SHGCs From a Single Intensity View," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 2, pp. 161-180, Feb. 1996, doi:10.1109/34.481541
Usage of this product signifies your acceptance of the Terms of Use.