Abstract
Systems of coupled, non-linear diffusion equations are pro- posed as a computational tool for grouping. Grouping tasks are divided into two classes - local and bilocal - and for each a prototypical set of equations is presented. It is shown how different cues can be used for grouping given these two blueprints plus cue-specific specialisations. Results are shown for intensity, texture orientation, stereo disparity, opti- cal flow, mirror symmetry, and regular textures. The proposed equations are particularly well suited for parallel implementations. They also show some interesting analogies with basic architectural characteristics of the cortex.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
L. Ambrosio, V. Tortorelli, Approximation of functionals depending on jumpls by elliptic fnctionals via T-convergence. Comm.. Pure and Appl. Math., vol.43, pp. 999–1036, 1990
A. Blake and A. Zisserman, Visual Reconstruction, MIT Press, 1987
G. Chaitin, Randomness and mathematical proof, Scientific American, Vol. 232, No. 5, pp. 47–52, 1975
S. Grossberg and D. Todorovic, Neural dynamics of 1-D and 2-D brightness perception: A unified model of classical and recent phenomena, Perception & Psychophysics, 43, 241–277, 1988
Horn B.K.P. and Schunck G.: Determining optical flow. AI. 17, 185–203, 1981.
B. Jenkins, Redundancy in the perception of bilateral symmetry in dot patterns, Perception & Psychophysics, Vol. 32, No. 2, pp. 171–177, 1982
E. Jones, Determinants of the cytoarchitecture of the cerebral cortex, ch. 1 in Signal and sense, local and global order in perceptual maps, eds. Edelman, Gall, and Cowan, pp. 3–50, Wiley-Liss, 1990
T. Kanade, Recovery of the 3-dimensional shape of an object from a single view, Arti_cial Intelligence, Vol.17, pp.75–116, 1981
D. Lowe, Perceptual Organization and Visual Recognition Stanford University technical report STAN-CS-84-1020, 1984
D. Marr and T. Poggio, A therory of human stereopsis, Proc. Royal Soc. B, 204, pp.301–328, 1979.
D. Mumford and J. Shah, Ootimal approximation by piecewise smooth functions and associated variational problems, Comm. on Pure and Applied Math., Vol.42, pp. 577–685, 1989
T. Papathomas, I. Kovacs, A. Gorea, and B. Julesz, A unified approach to the perception of motion, stereo, and static-flow patterns, Behavior Research Methods, Instruments, & Computers, Vol. 27, No. 4, pp. 419–432, 1995
P. Perona and J. Malik, Scale-Space and Edge Detection Using Anisotropic Diffusion, PAMI Vol.12, No.7, July 1990.
W. Phillips and W. Singer, In search of common foundations for cortical computation, Behavioral and Brain Sciences, Vol. 20, pp. 657–722, 1997
M. Proesmans, L. Van Gool, and A. Oosterlinck, Determination of optical flow and its discontinuities using non-linear diffusion, ECCV, 295–304, may 1994
M. Proesmans, E. Pauwels, and L. Van Gool, Coupled geometry-driven diffusion equations for low-level vision, in Geometry-Driven Diffusion in Computer Vision, Kluwer Academic Publishers, pp.191–228, 1994.
M. Proesmans, L. Van Gool, and A. Oosterlinck, Grouping through local, parallel interactions, SPIE Int. Symp. on Optical Science, Appl. of Digital Image Processing XVIII, Vol.2564, pp.458–469, 1995
J. Shah, Segmentation by non-linear diffusion. CVPR, 1991.
A. Treisman and G. Gelade, A feature integration theory of attention, Cognitive Psychology, Vol. 12, pp. 97–136, 1980
A. Treisman, Preattentive processing in vision, CVIP, 31, 156–177, 1985
A. Treisman, P. Cavanagh, B. Fischer, V. Ramachandran, and R. von der Heydt, Form perception and attention, striate cortex and beyond, in Visual Perception: The Neurophysiological Foundations, Academic Press, 1990
R. von der Heydt, E. Peterhans, and G. Baumgartner, Illusory contours and cortical neuron responses, Science, Vol.224, pp.1260–1262, 1984
M. Wertheimer, Laws of organization in perceptual forms, in A source-book of Gestalt Psychology, ed. D. Ellis, Harcourt, Brace and Co., pp.71–88, 1938
S. Zeki, Functional specialisation in the visual cortex: the generation of separate constructs and their multistage integration, ch. 4 in Signal and sense, local and global order in perceptual maps, eds. Edelman, Gall, and Cowan, pp. 85–130,Wiley-Liss, 1990
S. Zeki, A Vision of the Brain, Blackwell Scientific Publications, 1994.
S. Zucker, Early processes for orientation selection and grouping, in From Pixels to Predicates, ed. A. Pentland, pp.170–200, Ablex, New Jersey, 1986
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Proesmans, M., Van Gool, L. (1999). Grouping Based on Coupled Diffusion Maps. In: Shape, Contour and Grouping in Computer Vision. Lecture Notes in Computer Science, vol 1681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46805-6_12
Download citation
DOI: https://doi.org/10.1007/3-540-46805-6_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66722-3
Online ISBN: 978-3-540-46805-9
eBook Packages: Springer Book Archive