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A Shape From Shading Analysis for a Single Perspective Image of a Polyhedron
June 1989 (vol. 11 no. 6)
pp. 545-554
A shape-from-shading analysis for a single perspective image of a polyhedron is presented. Given a single perspective image of a polyhedron, the depth of any point of the polyhedron from the camera, the direction of the light source illuminating the polyhedron and the albedo of the polyhedron, a system of algebraic equations are derived, which, when combined with edge information, quantitatively describes the shape of the polyhedron. This analysis is best possible in the sense that if any component of what the author has assumed is omitted, no similar analysis can provide the same results.
[1] 545D. H. Ballard and C. M. Brown,Computer Vision. Englewood Cliffs, NJ: Prentice-Hall, 1982.[2] T. Banchoff, "Critical points and curvature for embedded polyhedra,"J. Differential Geometry, vol. 1, pp. 245-256, 1967.[3] S. T. Barnard, "Methods for interpreting perspective images," inProc. Image Understanding Workshop, Stanford Univ., Sept. 1982. pp. 193-203.[4] R. Burden and J. Faires,Numerical Analysis, 3rd ed. Boston, MA: Prindle, Weber&Schmidt, 1981.[5] S. Chen and M. Penna, "A geometric approach to motion analysis," inProc. Fourth Annu. Conf. Intelligent Systems and Machines, Oakland Univ., Rochester, MI, 1986, pp. 83-86.[6] S. Chen and M. Penna, "Recognizing deformations of nonrigid bodies," inProc. IEEE Comput. Soc. Conf. Computer Vision and Pattern Recognition, Miami, FL, 1986, pp. 452-455.[7] S. Chen and M. Penna, "Shape and correspondence," inProc. Intelligent Robots and Computer Vision: Fifth in a Series, SPIE 726, 1986, pp. 115-119.[8] S. Chen and M. Penna, "Shape and motion of nonrigid bodies,"Comput. Vision Graphics Image Processing, vol. 36, pp. 175-207, 1986.[9] M. Clowes, "On seeing things,"Artificial Intell., vol. 2, no. 1, pp. 79-116, 1971.[10] T. Homma, "On PL total curvature," inProc. Conf. Manifolds, Tokyo, Japan, 1970, pp. 111-116.[11] B. Horn, "Understanding image intensities,"Artificial Intell., vol. 8, pp. 203-231, 1977.[12] B. K. P. Horn,Robot Vision. Cambridge, MA: M.I.T. Press, 1986.[13] B. K. P. Horn, "Shape from shading: A method for obtaining the shape of a smooth opaque object from one view," MIT Project MAC Int. Rep. TR-79 and MIT AI Lab, Tech. Rep. 232, Nov. 1970.[14] D. A. Huffman, "Impossible objects as nonsense sentences," inMachine Intelligence, vol. 6, B. Meltzer and D. Michie, Eds. London: Edinburgh University Press.[15] K. Ikeuchi and B. Horn, "Numerical shape from shading and occluding boundaries,"Artificial Intell., vol. 17, pp. 141-184, 1981.[16] T. Kanade, "Recovery of the three-dimensional shape of an object from a single view,"Artificial Intell., vol. 17, pp. 409-460, 1981.[17] T. Kanade, "A theory of origami world,"Artificial Intell., vol. 13, pp. 279-311, 1980.[18] T. Kanade and J. Kender, "Mapping image properties into shape constraints: Skewed symmetry and affine-transformable patterns," inProc. IEEE Workshop Picture Data Description and Management, New York, NY, Aug. 1980, pp. 130-135.[19] A. Mackworth, "Interpreting pictures of polyhedral scenes,"Artificial Intell., vol. 4, pp. 121-137, 1973.[20] A. Mackworth, "Model-driven interpretation in intelligent vision systems,"Perception, vol. 5, pp. 349-370, 1976.[21] M. Penna, "Determining the position of a camera relative to that of a cube from a single perspective image," to be published.[22] M. Penna, "Local and semi-local shape from shading for a single perspective image," to be published.[23] M. Penna and S. Chen, "Shape from shading using multiple light sources,"Int. J. Intell., Syst., vol. 1, pp. 263-292, 1986.[24] M. Penna and S. Chen, "Spherical analysis in computer vision and image understanding," inImage Understanding in an Unstructured Environment, S. Chen, Ed., to be published.[25] M. A. Penna and R. R. Patterson,Projective Geometry and its Applications to Computer Projective Graphics. Englewood Cliffs, NJ: Prentice-Hall, 1986.[26] A. Pentland, "Local shading analysis,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 2, pp. 170-187, Sept. 1984.[27] T. Regge, "General relativity theory without coordinates,"Nuovo Cimento, vol. 19, no. 3, pp. 558-571, 1961.[28] K. Sugihara, "A necessary and sufficient condition for a picture to represent a polyhedral scene,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 2, pp. 578-586, Sept. 1984.[29] K. Sugihara, "Classification of impossible objects,"Perception, vol. 11, pp. 65-74, 1982.[30] K. Sugihara, "Picture language for skeletal polyhedra,"Comput. Graphics Image Processing, vol. 8, pp. 382-405, 1978.[31] A. Rosenfeld and A. Kak,Digital Image Processing. New York: Academic, 1986.[32] W. A. Richards, J. M. Rubin, and D. D. Hoffman, "Equation counting and the interpretation of sensory data,"Perception, vol. 11, pp. 557-576, 1982.[33] M. Spivak,A Comprehensive Introduction to Differential Geometry. Boston, MA: Publish or Perish Press, 1970.[34] D. Waltz, "Generating semantic descriptions from drawings of scenes with shadows," MAC-AI-TR-271, Mass. Inst. Technol., Cambridge, 1972.[35] J. A. Webb and J. K. Aggarwal, "Shape and correspondence,"Computer Vision, Graphics, Image Processing, vol. 21, pp. 145-160, 1983.
Index Terms:
picture processing; pattern recognition; shape from shading analysis; single perspective image; polyhedron; light source; algebraic equations; algebra; computational geometry; pattern recognition; picture processing
Citation:
M.A. Penna, "A Shape From Shading Analysis for a Single Perspective Image of a Polyhedron," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 6, pp. 545-554, June 1989, doi:10.1109/34.24790
