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B-spline Contour Representation and Symmetry Detection
November 1993 (vol. 15 no. 11)
pp. 1191-1197
The detection of edges is only one of many steps in the understanding of images. Further processing necessarily involves grouping operations between contours. We present a representation of edge contours by approximating B-splines and show that such a representation facilitates the extraction of symmetries between contours. Our representation is rich, compact, stable, and does not critically depend on feature extraction. We turn our attention to the detection of three types of symmetries: skew symmetries and parallel symmetries, which have proven to be of great importance in inferring shape from contour, and smooth local symmetries, which have been used for planar shape description. We show that our representation facilitates the computation of these symmetries.
[1] 1191H. Asada and M. Brady, "The curvature primal sketch,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 1, pp. 2-14, 1986.[2] D. H. Ballard and C. M. Brown,Computer Vision. Englewood Cliffs, NJ: Prentice-Hall, 1982.[3] R.H. Bartels, J.C. Beatty, and B.A. Barsky,An Introduction to Splines for Use in Computer Graphics and Geometric Modeling, Morgan Kaufmann Publishers, Los Altos, Calif., 1987.[4] H. Blum,A Transformation for Extracting New Descriptors of Shape. Cambridge, MA: MIT Press, 1967.[5] F. L. Bookstein, "The line-skeleton,"Comput. Graphics Image Processing, vol. 11, pp. 123-137, 1979.[6] M. Brady and H. Asada, "Smoothed local symmetries and their implementation,"Int. J. Robotics Res., vol. 3, no. 3, pp. 36-61, 1984.[7] R. Brent,Algorithms for Minimization without Derivatives. Englewood Cliffs, NJ: Prentice Hall, 1973.[8] R. A. Brooks, "Symbolic reasoning among 3-D models and 2-D images,"Artificial Intell., vol. 17, pp. 285-348, 1981.[9] J. F. Canny, "A computational approach to edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 1986.[10] J. H. Connell and M. Brady, "Generating and generalizing models of visual objects,"Artificial Intell., vol. 31, pp. 159-183, 1987.[11] G. Farin,Curves and Surfaces for Computer Aided Geometric Design, Academic Press, Boston, 1988.[12] H. Freeman, "On the encoding of arbitrary geometric configurations,"IRE Trans. Electron. Comput., pp. 260-268, June 1961.[13] S. A. Friedberg, "Finding axes of skewed symmetry,"Comput. Vision Graphics Image Processing, vol. 34, pp. 138-155, 1986.[14] P. J. Giblin and S. A. Brassett, "Local symmetry of plane curves,"Amer. Math. Monthly, vol. 92, pp. 689-707, 1985.[15] A. D. Gross and T. E. Boult, "SYMAN: a SYMmetry ANalyzer," inProc. IEEE Conf. Comput. Vision Patt. Recogn.(Maui, HI), 1991, pp. 744-746.[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] D. J. Kriegman and J. Ponce, "A new curve tracing algorithm and some applications," inCurves and Surfaces(P. J. Laurent, A. Le Mehaute, and L. L. Schumaker, Eds.). New York: Academic, 1990, pp. 1-4.[18] M. Leyton, "A process grammar for shape,"Artificial Intell. J., vol. 34, pp. 213-247, Mar. 1988.[19] D. Marimont, "A representation for image curves," inProc. Nat. Conf. Artificial Intell.(Austin, TX), 1984, pp. 237-242.[20] 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.[21] R. Mohan, "Perceptual organization for computer vision," Ph.D. Thesis, IRIS Rep., Univ. Southern Calif., 1989.[22] V. S. Nalwa, "Line-drawing interpretation: Bilateral symmetry,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, pp. 1117-1120, 1989.[23] V.S. Nalwa and E. Pauchon, "Edgel Aggregation and Description,"Computer Vision, Graphics, and Image Processing, Vol. 40, No. 1, Oct. 1987, pp. 79-94.[24] R. Nevatia and K. R. Babu, "Linear feature extraction and description,"Comput. Graphics Image Processing, vol. 13, pp. 257-269, 1980.[25] R. Nevatia and T. O. Binford, "Description and recognition of complex-curved objects,"Artificial Intell., vol. 8, pp. 77-98, 1977.[26] W. Perkins, "A model based vision system for industrial parts,"IEEE Trans. Comput., vol. C-27, pp. 126-143, Feb. 1978.[27] M. Plass and M. Stone, "Curve-fitting with piecewise parametric cubics,"ACM Trans. Comput. Graphics, vol. 17, no. 3, pp. 229-239, 1983.[28] J. Ponce, "On characterizing ribbons and finding skewed symmetries,"Comput. Vision Graphics Image Processing, vol. 52, pp. 328-340, 1990.[29] 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.[30] K. Rao, R. Nevatia, and G. Medioni, "Issues in shape description and an approach for working with sparse data," inWorkshop on Spatial Reasoning and Multi-Sensor Fusion(Chicago, IL), Oct. 1987, pp. 168-177.[31] W. A. Richards and D. D. Hoffman, "Codon constraints on closed 2D shapes,"Comput. Vision Graphics Image Processing, vol. 31, pp. 265-281, 1985.[32] H. Rom and G. Medioni, "Hierarchical decomposition and axial representation of shape," inProc. DARPA Image Understanding Workshop(San Diego), Jan. 1992, pp. 607-613.[33] H. Rom and G. Medioni, "Hierarchical decomposition and axial shape description," inProc. IEEE Conf. Comput. Vision Patt. Recogn.(Champaign, IL), June 1992, pp. 49-55.[34] H. Rom and G. Medioni, "Hierarchical decomposition and axial shape description,"IEEE Trans. Pattern Anal. Machine Intell., vol. 15, no. 10, pp. 972-981, Oct. 1993; also in Tech. Rep., Univ. of Southern Calif., Los Angeles, 1992.[35] A. Rosenfeld, "Axial representation of shape,"Comput. Vision Graphics Image Processing, vol. 33, pp. 156-173, 1986.[36] J. R. Rossignac and A. A. G. Requicha, "Piecewise-circular curves for geometric modeling,"IBM J. Res. Development, vol. 31, no. 3, pp. 296-313, 1987.[37] P. Saint-Marc, J. S. Chen, and G. Medioni, "Adaptive smoothing: A general tool for early vision,"IEEE Trans. Patt. Anal. Machine Intell., vol. 13, no. 6, pp. 514-529, 1991.[38] P. Saint-Marc and G. Medioni, "B-spline contour representation and symmetry detection," inProc. Euro. Conf. Comput. Vision(Antibes, France), 1990, pp. 604-606.[39] 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.[40] F. Ulupinar and R. Nevatia, "Shape from contour: Shgcs," inProc. 3rd ICCV, 1990, pp. 582-586.[41] F. Ulupinar and R. Nevatia, "Recovering shape from contour for constant cross section generalized cylinders," inProc. IEEE Conf. Comput. Vision Patt. Recogn.(Maui, HI), 1991, pp. 674-676.[42] L. Van Gool, P. Kempenaers, and T. Oosterlinck, "Recognition and semi-differential invariants," inProc. IEEE Conf. Comput. Vision Patt. Recogn.(Maui, HI), 1991, pp. 454-460, 1991.[43] S. Y. K. Yuen, "Shape from contour using symmetries," Tech. Rep. 141, School of Cognitive Sci., Univ. of Sussex, 1989.
Index Terms:
B-spline contour representation; symmetry detection; edge detection; edge contours; skew symmetries; parallel symmetries; shape from contour; smooth local symmetries; planar shape description; image recognition; splines (mathematics)
Citation:
P. Saint-Marc, H. Rom, G. Medioni, "B-spline Contour Representation and Symmetry Detection," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 11, pp. 1191-1197, Nov. 1993, doi:10.1109/34.244680
