Analysis of a Cooperative Stereo Algorithm

  • D. Marr
  • G. Palm
  • T. Poggio


Marr and Poggio (1976) recently described a cooperative algorithm that solves the correspondence problem for stereopsis. This article uses a probabilistic technique to analyze the convergence of that algorithm, and derives the conditions governing the stability of the solution state. The actual results of applying the algorithm to random-dot stereograms are compared with the probabilistic analysis. A satisfactory mathematical analysis of the asymptotic behaviour of the algorithm is possible for a suitable choice of the parameter values and loading rules, and again the actual performance of the algorithm under these conditions is compared with the theoretical predictions. Finally, some problems raised by the analysis of this type of “cooperative” algorithm are briefly discussed.


Probabilistic Analysis Invariant State Solution Plane Solution Layer Disparity Layer 


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  1. Eigen, M.: Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften 10, 465–523 (1971)CrossRefGoogle Scholar
  2. Haken,H.: Synergetics. Berlin-Heidelberg-New York: Springer 1977 Kawasaki,K.: Kinetics of Ising models. In: Phase transitions and critical phenomena, Vol. 2, pp. 443–501.Google Scholar
  3. Domb and Green eds., New York: Academic Press 1972Google Scholar
  4. Marr,D.: Simple memory: s theory for archicortex. Phil. Trans. Roy. Soc. 262, 23–81 (1971)CrossRefGoogle Scholar
  5. Marr,D.: A note on the computation of binocular disparity in a symbolic, low-level visual processor. M.I.T. A.I. Lab. Memo 12, 327, (1974)Google Scholar
  6. Marr,D.: Early processing of visual information. Phil. Trans. Roy. Soc. 275, 483–524 (1976)CrossRefGoogle Scholar
  7. Marr,D.: Representing visual information. AAAS 143rd Annual Meeting, Symposium on Some Mathematical Questions in Biology, February, (in press). Also available as M.I.T. A.I. Lab. Memo 415 (1977)Google Scholar
  8. Marr,D., Poggio,T.: Cooperative computation of stereo disparity. Science 194, 283–287 (1976)CrossRefGoogle Scholar
  9. Mostow: Mathemathical models for cell rearrangement. Newhaven, Yale University Press 1975Google Scholar
  10. Richter,P.H.: The network idea and the immune response. In: Theoretical Immunology, Bell, G. I., Perelson, A.S., Pimbley,G.H., eds. New York: M.Dekker 1976Google Scholar
  11. Wilson,H.R.: Hysteresis in binocular grating perception: contrast effects. Vision Res. (1977) (in press)Google Scholar
  12. Wilson,H. R., Cowan,J. D.: A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13, 55–80 (1973)CrossRefGoogle Scholar
  13. Wilson,K.G.: The renormalization group: Critical phenomena and the Kondo problem. Reviews Mod. Phys. 47, 773–840 (1975)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • D. Marr
    • 1
  • G. Palm
    • 2
  • T. Poggio
    • 2
    • 3
  1. 1.Department of PsychologyMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Max-Planck-Institut für Biologische KybernetikTübingenGermany
  3. 3.MPI für biolog. KybernetikTübingenFederal Republic of Germany

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