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Perception of 3-D Surfaces from 2-D Contours
January 1993 (vol. 15 no. 1)
pp. 3-18

Inference of 3-D shape from 2-D contours in a single image is an important problem in machine vision. The authors survey classes of techniques proposed in the past and provide a critical analysis. They show that two kinds of symmetries in figures, which are known as parallel and skew symmetries, give significant information about surface shape for a variety of objects. They derive the constraints imposed by these symmetries and show how to use them to infer 3-D shape. They also discuss the zero Gaussian curvature (ZGC) surfaces in depth and show results on the recovery of surface orientation for various ZGC surfaces.

[1] I. Beiderman, "Recognition by components: A theory of human image understanding,"Psycholog. Rev., vol. 94, no. 2, pp. 115-147, 1987.
[2] H.G. Barrow and J. M. Tenenbaum, "Interpreting line drawings as three dimensional surfaces,"Artif. Intell., vol. 17, pp. 75-116, 1981.
[3] M. Brady and A. Yuille, "An extremum principle for shape from contour,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, pp. 288-301, 1984.
[4] M.B. Clowes, "On seeing things,"Artif. Intell., vol. 2, no. 1, pp. 79-116, 1971.
[5] R. Horaud and M. Brady, "On the geometric interpretation of image contours,"Artif. Intell., vol. 37, pp. 333-353, 1988.
[6] D. A. Huffman, "Impossible objects as nonsense sentences,"Machine Intell., vol. 6, pp. 295-323, 1971.
[7] T. Kanade, "Recovery of the three-dimensional shape of an object from a single view,"Artif. Intell., vol. 17, pp. 409-460, 1981.
[8] R. Kashipati, "Shape description from sparse and imperfect data," Ph.D. thesis, Univ. of Southern California, 1988.
[9] T. Kanade and J. R. Kender, "Mapping image properties into shape constraints: Skew symmetry, affine transformable patterns, and the shape from texture paradigm," inHuman and Machine Vision(J. Beck, B. Hope, and A. Rosenfeld, Eds.). New York: Academic, 1983, pp. 237-257.
[10] J. J. Koenderink, "What does the occluding contour tell us about solid shape,"Perception, vol. 13, pp. 321-330, 1984.
[11] M. Lipschutz,Differential Geometry. New York: McGraw-Hill, 1969.
[12] A. K. Mackworth, "Interpreting pictures of polyhedral scenes,"Artif. Intell., vol. 4, pp. 121-137, 1973.
[13] R. Mohan and R. Nevatia, "Segmentation and description based on perceptual organization," inProc. IEEE Conf. Comput. Vision Patt. Recogn. (San Diego, CA), June 1989.
[14] G. Medioni and Y. Yasumoto, "Corner detection and curve representation using cubic B-splines,"Comput. Vision, Graphics, Image Processing, vol. 39, pp. 267-278, 1987.
[15] V. Nalwa, "Line-drawing interpretation: Bilateral symmetry,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, pp. 1117-1120, 1989.
[16] R. Nevatia and T. O. Binford, "Description and recognition of complex-curved objects,"Artif. Intell., vol. 8, pp. 77-98, 1977.
[17] J. Ponce, D. Chelberg, and W. B. Mann, "Invariant properties of straight homogeneous generalized cylinders and their contours,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 9, pp. 951-966, 1989.
[18] J. Ponce, "Ribbons, symmetries and skew symmetries, inProc. Image Understanding Workshop, 1988, pp. 1074-1079.
[19] S. A. Shafer, T. Kanade, and J. R. Kender, "Gradient space under orthography and perspective,"Comput. Vision Graphics Image Processing, vol. 24, pp. 182-199, 1983.
[20] K. A. Stevens, "The visual interpretations of surface contours,"Artif. Intell., vol. 17, pp. 47-73, 1981.
[21] F. Ulupinar, "Perception of 3-D shape from 2-D images of contours," Rep. IRIS 278, Univ. of Southern California, 1991.
[22] F. Ulupinar and R. Nevatia, "Using symmetries for analysis of shape from contour," inProc. 2nd ICCV, Tarpon Springs, FL, 1988, pp. 414-426.
[23] F. Ulupinar and R. Nevatia, "Perception of 3-D surfaces from 2-D contours," inProc. 10th Int Conf. Patt. Recogn.(Atlantic City, NJ), 1990, pp. 147-154.
[24] F. Ulupinar and R. Nevatia, "Shape from contour: Shgcs," inProc. 3rd ICCV, 1990, pp. 582-586.
[25] F. Ulupinar and R. Nevatia, "Constraint for interpretation of line drawings under perspective projection,"Comput. Vision Graphics Image Processing, vol. 52, pp. 674-676, 1991.
[26] I. Weiss, "3-D shape representation by contours,"Computer Vision, Graphics and Image Processing, no. 41, pp. 80-100, 1988.
[27] G. Xu and S. Tsuji, "Inferring surfaces from boundaries," inProc. 1st ICCV(London), 1987, pp. 716-720.

Index Terms:
3D shape inference; 2D contours; parallel symmetries; surface orientation recovery; image recognition; machine vision; skew symmetries; zero Gaussian curvature; computer vision; image recognition; inference mechanisms
F. Ulupinar, R. Nevatia, "Perception of 3-D Surfaces from 2-D Contours," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 1, pp. 3-18, Jan. 1993, doi:10.1109/34.184771
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