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Euclidean Group Invariant Computation of Stochastic Completion Fields Using Shiftable-Twistable Functions

  • John W. Zweck
  • Lance R. Williams
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1843)

Abstract

We describe a method for computing the likelihood that a completion joining two contour fragments passes through any given position and orientation in the image plane, that is, a method for completing the boundaries of partially occluded objects. Like computations in primary visual cortex (and unlike all previous models of contour completion in the human visual system), our computation is Euclidean invariant. This invariance is achieved in a biologically plausible manner by representing the input, output, and intermediate states of the computation in a basis of shiftable-twistable functions. The spatial components of these functions resemble the receptive fields of simple cells in primary visual cortex. Shiftable-twistable functions on the space of positions and directions are a generalization of shiftable-steerable functions on the plane.

Keywords

Visual Cortex Primary Visual Cortex Simple Cell Illusory Contour Occlude Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Blasdel, G., and Obermeyer, K., Putative Strategies of Scene Segmentation in Monkey Visual Cortex, Neural Networks, 7, pp. 865–881, 1994.CrossRefGoogle Scholar
  2. 2.
    Cowan, J.D., Neurodynamics and Brain Mechanisms, Cognition, Computation and Consciousness, Ito, M., Miyashita, Y. and Rolls, E., (Eds.), Oxford UP, 1997.Google Scholar
  3. 3.
    Daugman, J., Uncertainty Relation for Resolution in Space, Spatial Frequency, and Orientation Optimized by Two-dimensional Visual Cortical Filter, J. Opt. Soc. Am. A, 2, pp. 1160–1169, 1985.Google Scholar
  4. 4.
    Daugman, J., Complete Discrete 2-D Gabor Transforms by Neural Networks for Image Analysis and Compression, IEEE Trans. Acoustics, Speech, and Signal Processing 36(7), pp. 1,169–1,179, 1988.CrossRefGoogle Scholar
  5. 5.
    Eyesel, U. Turning a Corner in Vision Research, Nature, 399, pp. 641–644, 1999.CrossRefGoogle Scholar
  6. 6.
    Freeman, W., and Adelson, E., The Design and Use of Steerable Filters, IEEE Trans. PAMI, 13(9), pp. 891–906, 1991.Google Scholar
  7. 7.
    Gilbert, C.D., Adult Cortical Dynamics, Physiological Review, 78, pp. 467–485, 1998.Google Scholar
  8. 8.
    Grossberg, S., and Mingolla, E., Neural Dynamics of Form Perception: Boundary Completion, Illusory Figures, and Neon Color Spreading, Psychological Review, 92, pp. 173–211, 1985.CrossRefGoogle Scholar
  9. 9.
    Heitger, R. and ven der Heydt, R., A Computational Model of Neural Contour Processing, Figure-ground and Illusory Contours, Proc. of 4th Intl. Conf. on Computer Vision, Berlin, Germany, 1993.Google Scholar
  10. 10.
    von der Heydt, R., Peterhans, E. and Baumgartner, G., Illusory Contours and Cortical Neuron Responses, Science, 224, pp. 1260–1262, 1984.CrossRefGoogle Scholar
  11. 11.
    Iverson, L., Toward Discrete Geometric Models for Early Vision, Ph.D. dissertation, McGill University, 1993.Google Scholar
  12. 12.
    Kalitzin, S., ter Haar Romeny, B., and Viergever, M., Invertible Orientation Bundles on 2D Scalar Images, in Scale-Space Theory in Computer Vision, ter Haar Romeny, B., Florack, L., Koenderink, J. and Viergever, M., (Eds.), Lecture Notes in Computer Science, 1252, 1997, pp. 77–88.Google Scholar
  13. 13.
    Li, Z., A Neural Model of Contour Integration in Primary Visual Cortex, Neural Computation, 10(4), pp. 903–940, 1998.CrossRefGoogle Scholar
  14. 14.
    Marčelja, S. Mathematical Description of the Responses of Simple Cortical Cells, J. Opt. Soc. Am., 70, pp. 1297–1300, 1980.CrossRefGoogle Scholar
  15. 15.
    Mumford, D., Elastica and Computer Vision, Algebraic Geometry and Its Applications, Chandrajit Bajaj (ed.), Springer-Verlag, New York, 1994.Google Scholar
  16. 16.
    Parent, P., and Zucker, S.W., Trace Inference, Curvature Consistency and Curve Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, pp. 823–889, 1989.CrossRefGoogle Scholar
  17. 17.
    Shashua, A. and Ullman, S., Structural Saliency: The Detection of Globally Salient Structures Using a Locally Connected Network, 2nd Intl. Conf. on Computer Vision, Clearwater, FL, pp. 321–327, 1988.Google Scholar
  18. 18.
    Simoncelli, E., Freeman, W., Adelson E. and Heeger, D., Shiftable Multiscale Transforms, IEEE Trans. Information Theory, 38(2), pp. 587–607, 1992.CrossRefMathSciNetGoogle Scholar
  19. 19.
    Thornber, K.K. and Williams, L.R., Analytic Solution of Stochastic Completion Fields, Biological Cybernetics 75, pp. 141–151, 1996.zbMATHCrossRefGoogle Scholar
  20. 20.
    Thornber, K.K. and Williams, L.R., Orientation, Scale and Discontinuity as Emergent Properties of Illusory Contour Shape, Neural Information Processing Systems 11, Denver, CO, 1998.Google Scholar
  21. 21.
    Williams, L.R., and Jacobs, D.W., Stochastic Completion Fields: A Neural Model of Illusory Contour Shape and Salience, Neural Computation, 9(4), pp. 837–858, 1997, (also appeared in Proc. of the 5th Intl. Conference on Computer Vision (ICCV)’ 95, Cambridge, MA).CrossRefGoogle Scholar
  22. 22.
    Williams, L.R., and Jacobs, D.W., Local Parallel Computation of Stochastic Completion Fields, Neural Computation, 9(4), pp. 859–881, 1997.CrossRefGoogle Scholar
  23. 23.
    Williams, L.R. and Thornber, K.K., A Comparison of Measures for Detecting Natural Shapes in Cluttered Backgrounds, Intl. Journal of Computer Vision, 34(2/3), pp. 81–96, 1999.CrossRefGoogle Scholar
  24. 24.
    Wandell, B.A., Foundations of Vision, Sinauer Press, 1995.Google Scholar
  25. 25.
    Yen, S. and Finkel, L., Salient Contour Extraction by Temporal Binding in a Cortically-Based Network, Neural Information Processing Systems 9, Denver, CO, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • John W. Zweck
    • 1
  • Lance R. Williams
    • 1
  1. 1.Dept. of Computer ScienceUniversity of New MexicoAlbuquerqueUSA

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