Advertisement

Geometric saliency of curve correspondences and grouping of symmetric contours

  • Tat-Jen Cham
  • Roberto Cipolla
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1064)

Abstract

Dependence on landmark points or high-order derivatives when establishing correspondences between geometrical image curves under various subclasses of projective transformation remains a shortcoming of present methods. In the proposed framework, geometric transformations are treated as smooth functions involving the parameters of the curves on which the transformation basis points lie. By allowing the basis points to vary along the curves, hypothesised correspondences are freed from the restriction to fixed point sets. An optimisation approach to localising neighbourhood-validated transformation bases is described which uses the deviation between projected and actual curve neighbourhood to iteratively improve correspondence estimates along the curves. However as transformation bases are inherently localisable to different degrees, the concept of geometric saliency is proposed in order to quantise this localisability. This measures the sensitivity of the deviation between projected and actual curve neighbourhood to perturbation of the basis points along the curves. Statistical analysis is applied to cope with image noise, and leads to the formulation of a normalised basis likelihood. Geometrically salient, neighbourhood-validated transformation bases represent hypotheses for the transformations relating image curves, and are further refined through curve support recovery and geometrically-coupled active contours. In the thorough application of this theory to the problem of detecting and grouping affine symmetric contours, good preliminary results are obtained which demonstrate the independence of this approach to landmark points.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D.H. Ballard and C.M. Brown. Computer Vision. Prentice-Hall, New Jersey, 1982.Google Scholar
  2. 2.
    J.M. Brady. Seeds of perception. In Proc. 3rd Alvey Vision Conf., pages 259–265, Cambridge, Sep 1987.Google Scholar
  3. 3.
    T. J. Cham and R. Cipolla. Geometric saliency of curve correspondences and grouping of symmetric contours. Technical Report CUED/F-INFENG/TR 235, University of Cambridge, Oct 1995.Google Scholar
  4. 4.
    T. J. Cham and R. Cipolla. Symmetry detection through local skewed symmetries. Image and Vision Computing, 13(5):439–450, June 1995.Google Scholar
  5. 5.
    M. A. Fischler and H. C. Wolf. Locating perceptually salient points on planar curves. IEEE Trans. Pattern Analysis and Machine Intell., 16(2):113–129, Feb 1994.Google Scholar
  6. 6.
    R. Glachet, J.T. Lapreste, and M. Dhome. Locating and modelling a flat symmetrical object from a single perspective image. CVGIP: Image Understanding, 57(2):219–226, 1993.Google Scholar
  7. 7.
    C. Harris. Geometry from visual motion. In A. Blake and A. Yuille, editors, Active Vision. MIT Press, 1992.Google Scholar
  8. 8.
    J. L. Mundy and A. Zisserman. Geometric Invariance in Computer Vision. Artificial Intelligence. MIT Press, 1992.Google Scholar
  9. 9.
    P. Saint-Marc, H. Rom, and G. Medioni. B-spline contour representation and symmetry detection. IEEE Trans. Pattern Analysis and Machine Intell., 15(11):1191–1197, Nov 1993.Google Scholar
  10. 10.
    J. L. Turney, T. N. Mudge, and R. A. Volz. Recognizing partially occluded parts. IEEE Trans. Pattern Analysis and Machine Intell., 7(4):410–421, July 1985.Google Scholar
  11. 11.
    F. Ulupinar and R. Nevatia. Perception of 3-D surfaces from 2-D contours. IEEE Trans. Pattern Analysis and Machine Intell., 15(1):3–18, 1993.Google Scholar
  12. 12.
    L. J. Van Gool, T. Moons, E. Pauwels, and A. Oosterlinck. Semi-differential invariants. In J. L. Mundy and A. Zisserman, editors, Geometric Invariance in Computer Vision, pages 157–192. MIT Press, 1992.Google Scholar
  13. 13.
    G. A. W. West and P. L. Rosin. Using symmetry, ellipses and perceptual groups for detecting generic surfaces of revolution in 2D images. In Applications of Artificial Intelligence, volume 1964, pages 369–379. SPIE, 1993.Google Scholar
  14. 14.
    M. Zerroug and R. Nevatia. Using invariance and quasi-invariance for the segmentation and recovery of curved objects. In J.L. Mundy and A. Zisserman, editors, Proc. 2nd European-US Workshop on Invariance, pages 391–410, 1993.Google Scholar
  15. 15.
    A. Zisserman, D. A. Forsyth, J. L. Mundy, and C. A. Rothwell. Recognizing general curved objects efficiently. In J. L. Mundy and A. Zisserman, editors, Geometric Invariance in Computer Vision, pages 228–251. MIT Press, 1992.Google Scholar
  16. 16.
    A. Zisserman, J. Mundy, D. Forsyth, J. Liu, N. Pillow, C. Rothwell, and S. Utcke. Class-based grouping in perspective images. In Proc. 4th Int. Conf. on Computer Vision, pages 183–188, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Tat-Jen Cham
    • 1
  • Roberto Cipolla
    • 1
  1. 1.Department of EngineeringUniversity of CambridgeCambridgeEngland

Personalised recommendations