Abstract
A methodology is described for associating local invariant signature functions to smooth planar curves in order to enable their translation, rotation, and scale-invariant recognition from arbitrarily clipped portions. The suggested framework incorporates previous approaches, based on locating inflections, curvature extrema, breakpoints, and other singular points on planar object boundaries, and provides a systematic way of deriving novel invariant signature functions based on curvature or cumulative turn angle of curves. These new signatures allow the specification of arbitrarily dense feature points on smooth curves, whose locations are invariant under similarity transformations. The results are useful for detecting and recognizing partially occluded planar objects, a key task in low-level robot vision.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Asada, H., and Brady, M. 1986. The curvature primal sketch. IEEE Trans. Patt. Anal. Mach. Intell., PAMI 8: 2–14.
Ballard, D.H. 1981. Generalizing the Hough transform to detect arbitrary shapes. Patt. Recog., 13(2): 111–122.
Barrett, E.B., Payton, P., and Brill, M.H. 1991. Contributions to the theory of projective invariants for curves in two and three dimensions. Proc. DARPA/ESPRIT Workshop on Invariants in Vision, Reykjavik, Iceland, March.
Bruckstein, A.M., Holt, R.J., Netravali, A.N., and Richardson, T.J. 1991. Invariant signatures for planar shape recognition under partial occlusion, AT&T Bell Labs Tech. Memo, Murray Hill, NJ, October.
Bruckstein, A.M., and Netravali, A.N. 1990. On differential invariants of planar curves and recognizing partially occluded planar shapes. AT&T Bell Laboratories Tech. Memo, Murray-Hill, NJ, July; also in Proc. Workshop on Visual Form, Capri, May, 1991.
Cyganski, D., Orr, J.A., Cott, T.A., and Dodson, R.J. 1987. An affine transform invariant curvature function. Proc. Ist Intern. Conf. Comput. Vis., London, pp. 496–500.
Fischler, M.A., and Bolles, R.C. 1986. Perceptual organization and curve partitioning, IEEE Trans. Patt. Anal. Mach. Intell., PAMI 8: 100–105.
Guggenheimer, H.W. (1963). Differential Geometry. McGraw Hill, New York; Dover: New York.
Gottschalk, P.G., Turney, J.L., and Mudge, T.N.. 1989. Effeient recognition of partially visible objects using a logarithmic complexity matching technique. Intern. J. Robotics Res., 8(6): 110–131.
Gottschalk, P.G., and Mudge, T.N. 1988. Efficient encoding of local shape. Proc. SPIE, Intell. Robots Comput. Vis., 7: 46–56.
Hu, M.K., 1962. Visual pattern recognition by moment invariants. IRE Trans. Inform. Theory, IT 8: 179–187.
Huttenlocher, D.P., and Ullman, S. 1987. Object recognition using alignment. Proc. lst Intern. Conf. Comput. Vis., London, pp. 102–111.
Hong, J., and Wolfson, H. 1988. An improved model-based matching method using footprints. Proc. Intern. Conf. Patt. Recog., Rome, pp. 72–78.
Koenderink, J.J. 1990. Solid Shape. MIT Press: Cambridge, MA.
Katzir, N., Lindenbaum, M., and Porat, M. 1990. Planar curve segmentation for recognition of partially occluded shapes. Proc. 10th Intern. Conf. Patt. Recog., Atlantic City.
Kalvin, A., Schonberg, E., Schwartz, J.T. and Sharir, M. 1986. Two-dimensional model-based boundary matching using footprints. Intern. J. Robotics Res., 5(4): 38–55.
Lamdan, Y., and Wolfson, H.J. 1988. Geometric hashing: A general and efficient model-based recognition scheme. Proc. 2nd Intern. Conf. Comput. Vis., Tarpon Springs, Florida, pp. 238–249.
Ray, K.S., and Majumder, D. Dutta. 1989. Application of differential geometry to recognize and locate partially occluded objects. Patt. Recog. Lett., 9: 351–360.
Turney, J.L., Mudge, T.N., and Volz, R.A. 1985. Recognizing partially occluded parts. IEEE Trans. Patt. Anal. Mach. Intell., PAMI (7)4: 410–421.
Vaz, R.F., and Cyganski, D. 1990. Generation of affine invariant local contour feature data. Patt. Recog. Lett., 11: 479–483, July.
VanGool, L., Kempenaers, P., and Oosterlinck, A. 1991. Recognition and semi-differential invariants. Intern. Conf. Patt. Recog., Maui, Hawaii, June.
VanGool, L., Moons, T., Pauwels, R., and Oosterlinck, A. 1991. Semi-differential invariants. DARPA/ESPRIT Workshop on Invariants in Vision, Reykjavik, Iceland, March.
Weiss, I. 1988. Projective invariants of shapes, CAR Tech. Rept. TR-339, University of Maryland, January.
Weiss, I. 1991. Noise resistant invariants of curves. CAR Tech. Rept. TR-537, February; also Proc. DARPA/ESPRIT Workshop on Invariants in Vision, Reykjavik, Iceland, March 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bruckstein, A.M., Katzir, N., Lindenbaum, M. et al. Similarity-invariant signatures for partially occluded planar shapes. Int J Comput Vision 7, 271–285 (1992). https://doi.org/10.1007/BF00126396
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00126396