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Probabilistic relaxation: Potential, relationships and open problems

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1223))

Abstract

We discuss the recent developments in probabilistic relaxation techniques which are used as a tool for contextual sensory data interpretation. The successes of a range of applications of probabilistic relaxation reported in the literature are briefly reviewed. We show that the implementation of a probabilistic relaxation process by means of multilayer perceptron computation has implications on the neural net design methodology. Further, the relationship of probabilistic relaxation to the Hough transform is exposed.

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References

  1. P A Devijver and J Kittler, Pattern recognition: A statistical approach, Prentice-Hall, Englewood Cliffs, NJ, 1982.

    Google Scholar 

  2. J Besag, On the satatistical analysis of dirty pictures, Journal Royal Statist. Society, 48, Series B, 259–302, 1986.

    Google Scholar 

  3. S Geman and D Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI-6, 721–741, 1984.

    Google Scholar 

  4. D Geiger and F Girosi, Parallel and deterministic algorithms from MRF's: Surface reconstruction, IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI-13, 181–188, 1991.

    Google Scholar 

  5. S Kirkpatrick, C D Gellatt and M P Vecchi, Optimization by simulated annealing, Science, 220, 671–680, 1983.

    Google Scholar 

  6. A Blake, The least disturbance principle and weak constraints, Pattern Recognition Letters, 1, 393–399, 1983.

    Google Scholar 

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

    Google Scholar 

  8. C Koch, J Marroquin and A Yuille, Analog neuronal networks in early vision, Proc Nat. Academic Science, 83, 4263–4267, 1986.

    Google Scholar 

  9. A Witkin, D Terzopoulos and M Kass, Signal matching through scale space, Intern. Journal Computer Vision, 133–144, 1987.

    Google Scholar 

  10. A Rosenfeld, R Hummel and S Zucker, Scene labeling by relaxation operations, IEEE Trans System Man and Cybernetics, SMC-6, 420–433, 1976.

    Google Scholar 

  11. O Faugeras and M Berthod, Improving consistency and reducing ambiguity in stochastic labeling, IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI-3, 412–423, 1981.

    Google Scholar 

  12. J Kittler and J Illingworth, A review of relaxation labelling algorithms, Image and Vision Computing, 3, 206,216, 1985.

    Article  Google Scholar 

  13. R Hummel and S Zucker, On the foundations of relaxation labeling process, IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI-5, 267–286, 1983.

    Google Scholar 

  14. J Kittler and E R Hancock, Combining evidence in probabilistic relaxation, Intern. Journal of Pattern Recognition and Artificial Intelligence, 3, 29–51, 1989.

    Google Scholar 

  15. E R Hancock and J Kittler, Edge labeling using dictionary-based relaxation, IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI-12, 165–181, 1990.

    Google Scholar 

  16. J Kittler, W J Christmas and M Petrou, Probabilistic relaxation for matching problems in computer vision, Proc 4th Intern. Conference on Computer Vision, Berlin, 1993.

    Google Scholar 

  17. J Kittler, P Papachristou and M Petrou, Combining evidence in dictionary based probabilistic relaxation Proc 8th Scandinavian Conference on Image Analysis, Tromso, 1993.

    Google Scholar 

  18. D L Waltz, Understanding line drawings of scenes with shadows, in The Psychology of Computer Vision, P H Winston, ed., McGraw-Hill, New York, 1975.

    Google Scholar 

  19. E R Hancock and J Kittler, Discrete relaxation, Pattern Recognition, 23, 711–733, 1990.

    Article  Google Scholar 

  20. S Peleg and A Rosenfeld, Determining compatibility coefficients for curve enhancement relaxation processes, IEEE Trans Systems, Man and Cybernetics, SMC-8, 548–555, 1978.

    Google Scholar 

  21. S Zucker, R Hummel and A Rosenfeld, An application of relaxation labelling to line and curve enhancement, IEEE Tranc Computers, C-26, 394–404, 1977.

    Google Scholar 

  22. R M Haralick, An interpretation of probabilistic relaxation, Computer Vision, Graphics and Image Processing, 22, 388–395, 1983.

    Google Scholar 

  23. R L Kirby, A product rule relaxation method, Computer Graphics and Image Processing, 13, 158–189, 1985.

    Google Scholar 

  24. S Peleg, A new probabilistic relaxation scheme, IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI-2, 362–369, 1980.

    Google Scholar 

  25. E R Hancock and J Kittler, Relaxation refinement of intensity ridges, Proc 11th Internat. Conference on Pattern Recognition, 459–463, 1992.

    Google Scholar 

  26. W J Christmas, J Kittler and M Petrou, Structural matching in computer vision using probabilistic relaxation, IEEE Trans Pattern Analysis and Machine Intelligence, PAMI-17, 749–764, 1995.

    Article  Google Scholar 

  27. J Kittler, P Papachristou and M Petrou, Probabilistic relaxation in line post-processing, Proc Workshop on Statistical Methods in Pattern Recognition, Tromso, 1993.

    Google Scholar 

  28. D H Ballard, Generalising the Hough Transform to detect arbitrary shapes, Pattern Recognition, 13, 111–122, 1981.

    Article  Google Scholar 

  29. J Illingworth and J Kittler, A survey of the Hough Transform, Computer Vision, Graphics and Image Processing, 44, 87–116, 1988.

    Google Scholar 

  30. A Califano and R Mohan, Multidimensional indexing for recognising visual shapes, Proc. IEEE Conf. Computer Vision and Pattern Recognition, 28–34, 1991.

    Google Scholar 

  31. H M Lee, J Kittler and K C Wong, Generalised Hough Transform in object recognition, Proc. 11th International Conference on Pattern Recognition, 285–289, 1992.

    Google Scholar 

  32. Z Shao and J Kittler, Fuzzy non-iterative ARG labelling with multiple interpretations, Proc 13th Internat. Conf. on Pattern Recognition, II-B, 181–185, 1996.

    Google Scholar 

  33. W J Christmas, J Kittler and M Petrou, Probabilistic feature-labelling schemes: modelling compatibility coefficient distributions, Image and Vision Computing, 14, 617–625, 1996.

    Article  Google Scholar 

  34. M Pelillo and M Refice, Learning compatibility coefficients for relaxation labelling, IEEE Trans Pattern Analysis and Machine Intelligence, PAMI-16, 933–945, 1994.

    Article  Google Scholar 

  35. W J Christmas, J Kittler and M Petrou, Labelling 2-D geometric primitives using probabilistic relaxation: reducing the computational requirements, Electronic Letters, 32, 312–314, 1996.

    Article  Google Scholar 

  36. A J Stoddart, M Petrou and J Kittler, A new algorithm for probabilistic relaxation based on the Baum Eagon theorem, Proceedings of the 6th International Conference on Computer Analysis of Images and Patterns, V Hlavac and R Sara eds., 647–679, Springer-Verlag, Berlin, 1995.

    Google Scholar 

  37. W J Christmas, J Kittler and M Petrou, Analytical approaches to the neural network architecture design, in Pattern Recognition in Practice IV: Multiple Paradigms, Comparative Studies and Hybrid Systems, E S Gelsema and L Kanal Eds., 325–335, North Holland, Amsterdam 1994.

    Google Scholar 

  38. J Kittler, relaxation methods and their neural net implementation, From Statistics to Neural Networks, V Cherkasky and H Wechsler, Eds., Springer Verlag, Berlin, 1994.

    Google Scholar 

  39. P L Palmer, J Kittler and M Petrou, A Hough transform algorithm with a 2D hypothesis testing kernel, Proceedings of the 11th IAPR International Conference on Pattern Recognition, 1992.

    Google Scholar 

  40. J. Matas, R Marik and J Kittler, Colour-based object recognition under spectrally non-uniform illumination, Image and Vision Computing, 13, 663–669, 1995.

    Article  Google Scholar 

  41. J Princen, J Illingworth and J Kittler, Hypothesis testing: a framework for analysing and optimising Hough transform performance, IEEE Transactions on Pattern Analysis and Machine Intelligence, 16, 329–341, 1994.

    Article  Google Scholar 

  42. J Illingworth, G Jones, J Kittler, M Petrou and J Princen, Robust statistical methods of 2D and 3D image description, Annals of Mathematics and Artificial Intelligence, 10, 125–148, 1994.

    Article  Google Scholar 

  43. Z Shao and J Kittler, Shape Recognition Using Invariant Unary and Binary Relations, Workshop on Visual Form, Capri, 1997 (submitted).

    Google Scholar 

  44. W J Christmas, J Kittler and M Petrou, Error propagation for 2D-to-3D matching with application to underwater navigation, Proceedings of the Seventh British Machine Vision Conference, 555–564, 1996.

    Google Scholar 

  45. W J Christmas, J Kittler and M Petrou, Location of objects in a cluttered scene using probabilistic relaxation, In: Arcelli C, Cordelia LP, Sanniti di Baja G ed. Aspects of Visual Form Processing, 119–128, Singapore: World Scientific, 1994.

    Google Scholar 

  46. R C Wilson, A N Evans and E R Hancock, Relational matching by discrete relaxation, Image and Vision Computing, 13, 411–422, 1995.

    Article  Google Scholar 

  47. R C Wilson and E R Hancock, Relational matching with dynamic graph structures, Proceedings 5th Intern. Conf. Computer Vision, 450–456, Cambridge, 1995.

    Google Scholar 

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Authors and Affiliations

  1. Centre for Vision, Speech and Signal Processing, School of Electronic Engineering, Information Technology and Mathematics, University of Surrey, GU2 5XH, Guildford, UK

    Josef Kittler

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  1. Josef Kittler
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Marcello Pelillo Edwin R. Hancock

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© 1997 Springer-Verlag Berlin Heidelberg

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Kittler, J. (1997). Probabilistic relaxation: Potential, relationships and open problems. In: Pelillo, M., Hancock, E.R. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 1997. Lecture Notes in Computer Science, vol 1223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62909-2_93

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  • DOI: https://doi.org/10.1007/3-540-62909-2_93

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62909-2

  • Online ISBN: 978-3-540-69042-9

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