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.
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References
Blasdel, G., and Obermeyer, K., Putative Strategies of Scene Segmentation in Monkey Visual Cortex, Neural Networks, 7, pp. 865–881, 1994.
Cowan, J.D., Neurodynamics and Brain Mechanisms, Cognition, Computation and Consciousness, Ito, M., Miyashita, Y. and Rolls, E., (Eds.), Oxford UP, 1997.
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.
Daugman, J., Complete Discrete 2-D Gabor Transforms by Neural Networks for Image Analysis and Compression, IEEE Trans. Acoustics, Speech, and Signal Processing36(7), pp. 1,169–1,179, 1988.
Eyesel, U. Turning a Corner in Vision Research, Nature, 399, pp. 641–644, 1999.
Freeman, W., and Adelson, E., The Design and Use of Steerable Filters, IEEE Trans. PAMI, 13(9), pp. 891–906, 1991.
Gilbert, C.D., Adult Cortical Dynamics, Physiological Review, 78, pp. 467–485, 1998.
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.
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.
von der Heydt, R., Peterhans, E. and Baumgartner, G., Illusory Contours and Cortical Neuron Responses, Science, 224, pp. 1260–1262, 1984.
Iverson, L., Toward Discrete Geometric Models for Early Vision, Ph.D. dissertation, McGill University, 1993.
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.
Li, Z., A Neural Model of Contour Integration in Primary Visual Cortex, Neural Computation, 10(4), pp. 903–940, 1998.
Marčelja, S. Mathematical Description of the Responses of Simple Cortical Cells, J. Opt. Soc. Am., 70, pp. 1297–1300, 1980.
Mumford, D., Elastica and Computer Vision, Algebraic Geometry and Its Applications, Chandrajit Bajaj (ed.), Springer-Verlag, New York, 1994.
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.
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.
Simoncelli, E., Freeman, W., Adelson E. and Heeger, D., Shiftable Multiscale Transforms, IEEE Trans. Information Theory, 38(2), pp. 587–607, 1992.
Thornber, K.K. and Williams, L.R., Analytic Solution of Stochastic Completion Fields, Biological Cybernetics75, pp. 141–151, 1996.
Thornber, K.K. and Williams, L.R., Orientation, Scale and Discontinuity as Emergent Properties of Illusory Contour Shape, Neural Information Processing Systems11, Denver, CO, 1998.
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).
Williams, L.R., and Jacobs, D.W., Local Parallel Computation of Stochastic Completion Fields, Neural Computation, 9(4), pp. 859–881, 1997.
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.
Wandell, B.A., Foundations of Vision, Sinauer Press, 1995.
Yen, S. and Finkel, L., Salient Contour Extraction by Temporal Binding in a Cortically-Based Network, Neural Information Processing Systems9, Denver, CO, 1996.
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Zweck, J.W., Williams, L.R. (2000). Euclidean Group Invariant Computation of Stochastic Completion Fields Using Shiftable-Twistable Functions. In: Vernon, D. (eds) Computer Vision — ECCV 2000. ECCV 2000. Lecture Notes in Computer Science, vol 1843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45053-X_7
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DOI: https://doi.org/10.1007/3-540-45053-X_7
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