Skip to main content

Nonlinear Analog Networks for Image Smoothing and Segmentation

  • Chapter
Book cover Parallel Processing on VLSI Arrays

Abstract

Image smoothing and segmentation algorithms are frequently formulated as optimization problems. Linear and nonlinear (reciprocal) resistive networks have solutions characterized by an extremum principle. Thus, appropriately designed networks can automatically solve certain smoothing and segmentation problems in robot vision. This paper considers switched linear resistive networks and nonlinear resistive networks for such tasks. Following [1] the latter network type is derived from the former via an intermediate stochastic formulation, and a new result relating the solution sets of the two is given for the “zero temperature” limit. We then present simulation studies of several continuation methods that can be gracefully implemented in analog VLSI and that seem to give “good” results for these nonconvex optimization problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Geiger and F. Girosi, “Parallel and Deterministic Algorithms from MRF’s: Surface Reconstruction and Integration,” IEEE Trans. Pattern Analysis and Mach. Intell., forthcoming.

    Google Scholar 

  2. D. Geiger and A. Yuille, “A Common Framework for Image Segmentation,” in Int. Jour. Comp. Vision, forthcoming.

    Google Scholar 

  3. S. Geman and D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. PAMI-6 (6), 1984, pp. 721–741.

    Article  MATH  Google Scholar 

  4. J.L. Marroquin. “Optimal Bayesian Estimators for Image Segmentation and Surface Reconstruction,” MIT AI Laboratory Memo 839, April 1985.

    Google Scholar 

  5. F.S. Cohen and D.B. Cooper, “Simple Parallel Hierarchical and Relaxation Algorithms for Segmenting Noncausal Markovian Random Fields,” IEEE Trans. PAMI-9 (2), 1987, pp. 195–219.

    Article  Google Scholar 

  6. J. Marroquin, S. Mitter, and T. Poggio, “Probabilistic Solution of Ill-Posed Problems in Computational Vision,” Jour. Amer. Stat. Assoc. (Theory and Methods), vol. 82, no. 397, 1987, pp. 76–89.

    Article  MATH  Google Scholar 

  7. A. Blake and A. Zisserman, Visual Reconstruction, Cambridge, MA: MIT Press, 1987.

    Google Scholar 

  8. A. Blake, “Comparison of the Efficiency of Deterministic and Stochastic Algorithms for Visual Reconstruction,” IEEE Trans. PAMI-11 (1), 1989, pp. 2–12.

    Article  Google Scholar 

  9. P. Perona and J. Malik, “Scale Space and Edge Detection Using Anisotropic Diffusion,” IEEE Trans. PAMI-12 (7), 1990, pp. 629–639.

    Article  Google Scholar 

  10. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, New York: Academic Press, 1970.

    MATH  Google Scholar 

  11. C. Koch, J. Marroquin, and A. Yuille, “Analog ‘Neuronal’ Networks in Early Vision,” Proc. Natl. Acad. Sci. USA, vol. 83, 1986, pp. 4263–4267.

    Article  MathSciNet  Google Scholar 

  12. D.W. Tank and J.J. Hopfield, “Simple ‘Neural’ Optimization Networks: An A/D Converter, Signal Decision Circuit, and a Linear Programming Circuit,” IEEE Trans. CAS-33(5), 1986.

    Google Scholar 

  13. D. Terzopoulos, “Multigrid Relaxation Methods and the Analysis of Lightness, Shading, and Flow,” MIT AI Laboratory Memo 803, October 1984.

    Google Scholar 

  14. W.D. Hillis, The Connection Machine, Cambridge, MA: MIT Press, 1985.

    Google Scholar 

  15. C.A. Mead, Analog VLSI and Neural Systems, Reading, MA: Addison-Wesley, 1988.

    Google Scholar 

  16. J. Harris, C. Koch, J. Luo, and J. Wyatt, “Resistive Fuses: Analog Hardware for Detecting Discontinuities in Early Vision,” in Analog VLSI Implementation of Neural Systems, C. A. Mead and M. Ismail, eds., Boston: Kluwer, 1989.

    Google Scholar 

  17. J. Harris, C. Koch, and J. Luo, “A Two-Dimensional Analog VLSI Circuit for Detecting Discontinuities in Early Vision,” Science, vol. 248, 1990, pp. 1209–1211.

    Article  Google Scholar 

  18. J. Harris, C. Koch, E. Staats, and J. Luo, “Analog Hardware for Detecting Discontinuities in Early Vision,” Int. J. Comp. Vision, vol. 4, 1990, pp. 211–223.

    Article  Google Scholar 

  19. T. Poggio and C. Koch, “Ill-Posed Problems in Early Vision: From Computational Theory to Analogue Networks,” Proc. Roy. Soc. Land. B 226, 1985, pp. 303–323.

    Article  MATH  Google Scholar 

  20. B.K.P. Horn, “Parallel Networks for Machine Vision,” MIT AI Laboratory Memo 1071, August 1988.

    Google Scholar 

  21. W. Millar, “Some General Theorems for Non-Linear Systems Possessing Resistance,” Phil. Mag., 1951, pp. 1150–1160.

    Google Scholar 

  22. I. Elfadel, “Note on a Switching Network for Image Segmentation,” unpublished manuscript, October 1988.

    Google Scholar 

  23. P.M. Hart, “Reciprocity, Power Dissipation, and the Thevenin Circuit,” IEEE Trans. CAS-33(7), 1986, pp. 716–718.

    Google Scholar 

  24. P. Cristea, F. Spinei, and R. Tuduce, “Comments on ‘Reciprocity, Power Dissipation, and the Thevenin Circuit,’” IEEE Trans. CAS-34 (10), 1987, pp. 1255–1257.

    Article  Google Scholar 

  25. P. Penfield, Jr., R. Spence, and S. Duinker, Tellegen’s Theorem and Electrical Networks, Cambridge, MA: MIT Press, 1970.

    Google Scholar 

  26. B.D.H. Tellegen, “A General Network Theorem with Applications,” Philips Res. Kept. 7, 1952, pp. 259–269.

    MathSciNet  MATH  Google Scholar 

  27. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd Edition, New York: McGraw-Hill, 1984.

    MATH  Google Scholar 

  28. A. Lumsdaine, M. Silveira, and J. White, “Simlab User’s Guide,” to be published as an MIT memo.

    Google Scholar 

  29. A. Lumsdaine, M. Silveira, and J. White, “CMVSIM User’s Guide,” to be published as an MIT memo.

    Google Scholar 

  30. L.M. Silveira, A. Lumsdaine, and J.K. White, “Parallel Simulation Algorithms for Grid-Based Analog Signal Processors,” Proceedings of the International Conference on Computer Aided Design, pp. 442–445, Santa Clara, CA, 1990.

    Google Scholar 

  31. T. Richardson, “Scale Independent Piecewise Smooth Segmentation of Images Via Variational Methods,” MIT Laboratory for Information and Decision Systems Technical Report LIDS-TH-1940, February 1990.

    Google Scholar 

  32. A. Witkin, “Scale-Space Filtering,” International Joint Conference on Artificial Intelligence, pp. 1019–1021, Karlsruhe, 1983.

    Google Scholar 

  33. H. Keller, “Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems,” in Applications of Bifurcation Theory, P. Rabinowitz, ed., New York: Academic Press, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media, New York

About this chapter

Cite this chapter

Lumsdaine, A., Wyatt, J.L., Elfadel, I.M. (1991). Nonlinear Analog Networks for Image Smoothing and Segmentation. In: Nossek, J.A. (eds) Parallel Processing on VLSI Arrays. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4036-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-4036-6_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6805-2

  • Online ISBN: 978-1-4615-4036-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics