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Computing the Perspective Projection Aspect Graph of Solids of Revolution
February 1993 (vol. 15 no. 2)
pp. 109-128

An algorithm for computing the aspect graph for a class of curved-surface objects based on an exact parcellation of 3-D viewpoint space is presented. The object class considered is solids of revolution. A detailed analysis of the visual events for this object class is given, as well as an algorithm for constructing the aspect graph. Numerical search techniques, based on a geometric interpretation of the visual events, have been devised to determine those visual event surfaces that cannot be calculated directly. The worst-case complexity of the number of cells in the parcellation of 3-D viewpoint space, and, hence, the number of nodes in the aspect graph, is O(N/sup 4/), where N is the degree of a polynomial that defines the object shape. A summary of the results for 20 different object descriptions is presented, along with a detailed example for a flower vase.

[1] K. Bowyer, D. Eggert, J. Stewman, and L. Stark, "Developing the aspect graph representation for use in image understanding," inProc. 1989 Image Understanding Workshop, 1989, pp. 831-849.
[2] K. W. Bowyer and C. R. Dyer, "Aspect graphs: An introduction and survey of recent results,"Int. J. Imaging Syst. Technol., vol. 2, pp. 315-328, 1990.
[3] J. Callahan and R. Weiss, "A model for describing surface shape," inProc. Conf. Comput. Vision Patt. Recogn., 1985, pp. 240-245.
[4] I. Chakravarty and H. Freeman, "Characteristic views as a basis for three-dimensional object recognition," inProc. SPIE: Robot Vision, 1982, pp. 37-45, vol. 336.
[5] S. Chen and H. Freeman, "Computing characteristic views of quadric-surfaced solids," inProc. 10th Int. Conf. Patt. Recogn., 1990.
[6] D. Eggert and K. Bowyer, "Computing the orthographic projection aspect graph of solids of revolution," inProc. IEEE Workshop Interpretation of 3D Scenes, Nov. 1989, pp. 102-108.
[7] D. Eggert, "Aspect graphs of solids of revolution," Doctoral dissertation, Univ. of South Florida, 1991.
[8] J. J. Koenderink and A. J. van Doorn, "The singularities of the visual mapping,"Biolog. Cybern., vol. 24, pp. 51-59, 1976.
[9] J. J. Koenderink and A. J. Van Doorn, "The internal representation of solid shape with respect to vision,"Biolog. Cybern., vol. 32, pp. 211-216, 1979.
[10] J. J. Koenderink, "What does occluding contour tell us about solid shape?",Perception, vol. 12, pp. 321-330, 1984.
[11] D. Kriegman and J. Ponce, "Computing exact aspect graphs of curved objects: Solids of revolution,"Int. J. Comput. Vision, vol. 5, pp. 119-135, 1990.
[12] J. Malik, "Interpreting line drawings of curved objects,"Int. J. Comput. Vision, vol. 1, pp. 73-103, 1987.
[13] V. Nalwa, "Line-drawing interpretation: Straight lines and conic sections,"IEEE Trans. Patt. Anal. Machine Intell., vol. 10, pp. 514-529, 1988.
[14] J. Ponce and D. Chelberg, "Finding the cusps and limbs of generalized cylinders,"Int. J. Comput. Vision, vol. 1, pp. 195-210, 1987.
[15] J. Ponce and D. Kriegman, "Computing exact aspect graphs of curved objects: Parametric surfaces," inProc. 8th Nat. Conf. Artificial Intell., 1990, pp. 1074-1079.
[16] F. P. Preparata and M. I. Shamos,Computational Geometry, an Introduction. New York: Springer-Verlag, 1985.
[17] J.H. Rieger, "On the classification of views of piecewise smooth objects,"Image Vision Comput., vol. 5, no. 2, pp. 91-97, May 1987.
[18] J. H. Rieger, "The geometry of view space opaque objects bounded by smooth surfaces,"Artificial Intell., vol. 44, pp. 1-40, 1990.
[19] J. H. Rieger, "Global bifurcation sets and stable projections of nonsingular algebraic surfaces,"Int. J. Comput. Vision, vol. 7, pp. 171-194, 1992.
[20] M. Y. Sallam, J. S. Stewman, and K. W. Bowyer, "Computing the visual potential of articulated assemblies," inProc. 3rd Int. Conf. Comput. Vision, 1990, pp. 636-643.
[21] S. A. Shafer,Shadows and Silhouettes in Computer Vision. Boston: Kluwer, 1985.
[22] T. Sripradisvarakul and R. Jain, "Generating aspect graphs for curved objects," inProc. IEEE Workshop Interpretation of 3D Scenes, Nov. 1989, pp. 109-115.

Index Terms:
3D viewpoint space; perspective projection aspect graph; solids of revolution; curved-surface objects; exact parcellation; visual events; aspect graph; geometric interpretation; worst-case complexity; object descriptions; computer vision; graph theory; image recognition
D. Eggert, K. Bowyer, "Computing the Perspective Projection Aspect Graph of Solids of Revolution," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 2, pp. 109-128, Feb. 1993, doi:10.1109/34.192483
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