This Article 
 Bibliographic References 
 Add to: 
Parts of Visual Form: Computational Aspects
March 1995 (vol. 17 no. 3)
pp. 239-251

Abstract—Underlying recognition is an organization of objects and their parts into classes and hierarchies. A representation of parts for recognition requires that they be invariant to rigid transformations, robust in the presence of occlusions, stable with changes in viewing geometry, and be arranged in a hierarchy. These constraints are captured in a general framework using notions of a PART-LINE and a PARTITIONING SCHEME. A proposed general principle of “form from function” motivates a particular partitioning scheme involving two types of parts, NECK-BASED and LIMB-BASED, whose psychophysical relevance was demonstrated in [39]. Neck-based parts arise from narrowings in shape, or the local minima in distance between two points on the boundary, while limb-based parts arise from a pair of negative curvature minima which have “co-circular” tangents. In this paper, we present computational support for the limb-based and neck-based parts by showing that they are invariant, robust, stable and yield a hierarchy of parts. Examples illustrate that the resulting decompositions are robust in the presence of occlusion and clutter for a range of man-made and natural objects, and lead to natural and intuitive parts which can be used for recognition.

[1] H. Asada and M. Brady, “The Curvature Primal Sketch,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, pp. 2-14, 1986.
[2] F. Attneave,“Some informational aspects of visual perception,” Psych. Review, vol. 61, pp. 183-193, 1954.
[3] R. Bajcsy and F. Solina,“Three-dimensional object representation revisited,” ICCV1987 [16], pp. 231-240.
[4] I. Biederman,“Recognition by components,” Psych. Review, vol. 94, pp. 115-147, 1987.
[5] T.O. Binford,“Visual perception by computer,” IEEE Conference on Systems and Control, December 1971.
[6] H. Blum,“Biological shape and visual science,” Journal Theor. Biol., vol. 38, pp. 205-287, 1973.
[7] H. Blum and R.N. Nagel,“Shape description using weighted symmetric axis features,” Pattern Recognition, vol. 10, pp. 167-180, 1978.
[8] M. Brady,W.E.L. Grimson,, and D.J. Langridge,“Shape encoding and subjective contours,” Proc. National Conf. on Artificial Intelligence, pp. 15-17, 1980.
[9] M.L. Braunstein,D.D. Hoffman,, and A. Saidpour,“Parts of visual objects: an experimental test of the minima rule,” Perception, vol. 18, pp. 817-826, 1989.
[10] P. Danielsson,“Euclidean distance mapping,” Computer Graphics and Image Processing, vol. 14, pp. 227-248, 1980.
[11] H. Freeman,“Shape description via the use of critical points,” Pattern Recognition, vol. 10, pp. 159-166, 1978.
[12] J. Gibson,The Perception of the Visual World, Riverside Press, 1950.
[13] A. Guzmán,“Decomposition of a visual scene into three-dimensional bodies,” Automatic Interpretation and Classification of Images,New Yor: Academic Press, 1969.
[14] D.D. Hoffman and W.A. Richards,“Parts of recognition,” Cognition, vol. 18, pp. 65-96, 1985.
[15] B.K.P. Horn,“The curve of least energy,” ACM Trans. Mathematical Software, vol. 5, no. 4, pp. 442-460, December 1983.
[16] First International Conference on Computer Vision (London, England, June 8-11, 1987),Washington, D.C..: IEEE Computer Society Press, 1987.
[17] G. Kanizsa,Organization in Vision: Essays on Gestalt Perception,New York: Praeger, 1979.
[18] B.B. Kimia,A.R. Tannenbaum,, and S.W. Zucker,Entropy Scale-Space,New York: Plenum Press, May 1991, pp. 333-344.
[19] —,“The shape triangle: Parts, protrusions, and bends,” Technical Report TR-92-15, McGill University Research Center for Intelligent Machines, 1992.
[20] —,“Shapes, shocks, and deformations, I: The components of shape and the reaction-diffusion space,” International Journal of Computer Vision, To Appear, 1994.
[21] J.J. Koenderink and A.J. van Doorn,“The shape of smooth objects and the way contours end,” Perception, vol. 11, pp. 129-137, 1982.
[22] Y.G. Leclerc,“Constructing simple stable descriptions for image partitioning,” International Journal of Computer Vision, vol. 3, pp. 73-102, 1989.
[23] M. Leyton, "Symmetry-Curvature Duality," Computer Vision, Graphics, and Image Processing, vol. 38, pp. 327-341, 1987.
[24] M. Leyton, "A Process-Grammar for Shape," Artificial Intelligence, vol. 34, pp. 213-247, 1988.
[25] —,“Inferring causal history from shape,” Cognitive Science, vol. 13, pp. 357-387, 1989.
[26] —,Symmetry, Causality, Mind,Cambridge, Mass.: MIT Press, April 1992.
[27] A. Linnér,“Steepest descent as a tool to find critical points of∫κ2defined on curves in the plane with arbitrary types of boundary conditions,” Geometric Analysis and Computer Graphics,New York: Springer-Verlag, 1988, pp. 127-138.
[28] D. Marr and K.H. Nishihara,“Representation and recognition of the spatial organization of three dimensional structure,” Proceedings of the Royal Society of London, vol. 200, pp. 269-294, 1978.
[29] R. Nevatia and T.O. Binford,“Description and recognition of curved objects,” Artificial Intelligence, vol. 8, pp. 77-98, 1977.
[30] M. Nitzberg, D. Mumford, and T. Shiota, “Filtering, Segmentation and Depth Filtering, Segmentation and Depth,” Lecture Notes in Computer Science, vol. 662, 1993.
[31] P. Parent and S.W. Zucker, “Trace Inference, Curvature Consistency and Curve Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 8, pp. 823-839, 1989.
[32] A. Pentland,“Recognition by parts,” ICCV1987 [16].
[33] A. Pentland,“Part segmentation for object recognition,” Neural Computation, vol. 1, pp. 82-91, 1989.
[34] U. Ramer,“An iterative procedure for the polygonal approximation of plane curves,” CVGIP, vol. 1, no. 3, pp. 244-256, 1972.
[35] W. Richards,B. Dawson,, and D. Whittington,“Encoding contour shape by curvature extrema,” Journal of Optical Society of America, vol. 3, no. 9, pp. 1483-1489, 1986.
[36] W. Richards and D.D. Hoffman,“Codon constraints on closed 2d shapes,” CVGIP, vol. 31, no. 2, pp. 156-177, 1985.
[37] W. Richards,J. Koenderink,, and D. Hoffman,“Inferring three dimensional shapes from two-dimensional silhouettes,” Journal of Optical Society of America, vol. 4, no. 7, pp. 1168-1175, 1987.
[38] L. Shapiro and R. Haralick,“Decomposition of two-dimensional shapes by graph-theoretic clustering,” IEEE PAMI, vol. 1, pp. 10-20, 1979.
[39] K. Siddiqi,K.J. Tresness,, and B.B. Kimia,“Parts of visual form: Ecological and psychophysical aspects,” Technical Report LEMS 104, LEMS, Brown University, June 1992.
[40] S. Ullman,“The shape of subjective contours and a model for their generation,” Biological Cybernetics, vol. 25, pp. 1-6, 1976.
[41] D.M. Wuescher and K.L. Boyer,“Robust contour decomposition using a constant curvature criterion,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 1, pp. 41-51, 1991.

Index Terms:
Parts, recognition, invariance, robustness, stability, salience, scale.
Kaleem Siddiqi, Benjamin B. Kimia, "Parts of Visual Form: Computational Aspects," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 3, pp. 239-251, March 1995, doi:10.1109/34.368189
Usage of this product signifies your acceptance of the Terms of Use.