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Differential Invariants of Planar Curves and Recognizing Partially Occluded Shapes

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Visual Form

Abstract

Viewing transformations like similarity, affine and projective maps may distort planar shapes considerably. However it is possible to associate local invariant signature functions to smooth boundaries that enable recognition of distorted shapes even in case of partial occlusion. The derivation of signature functions, generalizing the intrinsic curvature versus arclength representation in case of rigid motions in the plane, is based on differential invariants associated to viewing transformations.

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References

  1. K. Abter, W.E. Snyder, H. Burkhardt and G. Hirzinger, “Application of Affine Invariant Fourier Descriptors to Recognition of 3D Objects”, IEEE Trans. on Pattern Recognition and Machine Intelligence, IEEE PAMI-12/7, pp. 640-647, July 1990.

    Google Scholar 

  2. Su Buchin, “Affine Differential Geometry”, Science Press, Beijing, China 1983; Gordon and Breach Science Publishers, New York.

    MATH  Google Scholar 

  3. A.M. Bruckstein, N. Katzir, M. Lindenbaum and M. Porat, “Similarity Invariant Recognition of Partially Occluded Planar Curves and Shapes”, Technion: CIS Report 9003, June 1990.

    Google Scholar 

  4. A.M. Bruckstein and A.N. Netravali “On Differential Invariants of Planar Curves and Recognizing Partially Occluded Planar Shapes”, AT&T Technical Memorandum, Bell Laboratories at Murray Hill, July 1990.

    Google Scholar 

  5. D. Cyganski and J. A. Orr, “Applications of Tensor Theory to Object Recognition and Orientation Determination”, IEEE Trans. on Pattern Recognition and Machine Intelligence, Vol PAMI-7/6, pp. 662–672, Nov. 1988.

    Google Scholar 

  6. D. Cyganski, J.A. Orr, T.A. Cott and R.J. Dodson, “An Affine Transform Invariant Curvature Function”, Proceedings of the First ICCV, London, pp. 496-500, 1987.

    Google Scholar 

  7. H. W. Guggenheimer, “Differential Geometry”, McGraw Hill, New York, 1963.

    MATH  Google Scholar 

  8. E. P. Lane, “A Treatise on Projective Differential Geometry”, University of Chicago Press, 1941.

    Google Scholar 

  9. E. J. Wilczynski, “Projective Differential Geometry of Curves and Ruled Surfaces”, Leipzig: Teubner, 1906.

    Google Scholar 

  10. I. Weiss, “Projective Invariants of Shapes”, Center for Aut. Res. Report, CAR-TR-339, January 1988.

    Google Scholar 

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© 1992 Springer Science+Business Media New York

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Bruckstein, A.M., Netravali, A.N. (1992). Differential Invariants of Planar Curves and Recognizing Partially Occluded Shapes. In: Arcelli, C., Cordella, L.P., di Baja, G.S. (eds) Visual Form. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0715-8_10

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  • DOI: https://doi.org/10.1007/978-1-4899-0715-8_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-0717-2

  • Online ISBN: 978-1-4899-0715-8

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