Rate of convergence of the Swendsen-Wang dynamics in image segmentation problems : a theoretical and experimental study

Isabelle Gaudron

ESAIM: Probability and Statistics (1997)

  • Volume: 1, page 259-284
  • ISSN: 1292-8100

How to cite

top

Gaudron, Isabelle. "Rate of convergence of the Swendsen-Wang dynamics in image segmentation problems : a theoretical and experimental study." ESAIM: Probability and Statistics 1 (1997): 259-284. <http://eudml.org/doc/104235>.

@article{Gaudron1997,
author = {Gaudron, Isabelle},
journal = {ESAIM: Probability and Statistics},
keywords = {Metropolis relaxation; Swendsen-Wang dynamics; image segmentation problems},
language = {eng},
pages = {259-284},
publisher = {EDP Sciences},
title = {Rate of convergence of the Swendsen-Wang dynamics in image segmentation problems : a theoretical and experimental study},
url = {http://eudml.org/doc/104235},
volume = {1},
year = {1997},
}

TY - JOUR
AU - Gaudron, Isabelle
TI - Rate of convergence of the Swendsen-Wang dynamics in image segmentation problems : a theoretical and experimental study
JO - ESAIM: Probability and Statistics
PY - 1997
PB - EDP Sciences
VL - 1
SP - 259
EP - 284
LA - eng
KW - Metropolis relaxation; Swendsen-Wang dynamics; image segmentation problems
UR - http://eudml.org/doc/104235
ER -

References

top
  1. BESAG, J. and Green, P. J. ( 1993). Spatial statistics and bayesian computation. J. R. Statis. Soc. B 55 25-37. Zbl0800.62572MR1210422
  2. BESAG, J., GREEN, P. J., HIGDON, D. and MENGERSEN, K. ( 1995). Bayesian computation and stochastic systems. Statistical Science 10 3-66. Zbl0955.62552MR1349818
  3. DEUSCHEL, J.-D. and MAZZA, C. ( 1994). L2 convergence of time nonhomogeneous Markov processes: I. Spectral estimates. Ann. Appl. Prob. 4 1012-1056. Zbl0819.60063MR1304771
  4. DIACONIS, P. and STROOCK, D. ( 1991). Geometric bounds for eigenvalues of Markov chains. Ann. Appl. Prob. 1 36-61. Zbl0731.60061MR1097463
  5. FREIDLIN, M. I. and WENTZELL, A. D. ( 1984). Random perturbations of dynamical systems, 260, Springer-Verlag. Zbl0522.60055MR722136
  6. GAUDRON, I. and TROUVÉ, A. ( 1996). Fluctuations of empirical means at low temperature for finite Markov chains with rare transitions in the general case. Preprint CMLA, Cachan, France. MR1633578
  7. GEMAN, D. ( 1990). Ch. Random fields and inverse problems in imaging. Lectures on Probability Theory and Statistics. XVIIIème École d'Eté de Probabilités de Saint-Flour, Lecture Notes in Mathematics, Springer-Verlag. Zbl0718.60119MR1100283
  8. GEMAN, D., GEMAN, S., and GRAFFIGNE, C. ( 1986). Locating texture and object boundaries, in Pattern Recognition Theory and Applications, Devijver ed., NATO ASI, Springer-Verlag, Heidelberg. 
  9. GRAFFIGNE, C. ( 1987). Experiments in texture analysis and segmentation. PhD thesis, Brown University. 
  10. GRAY, A. ( 1994). Simulating posterior Gibbs distributions: A comparison of the Swendsen-Wang and Gibbs sampler methods. Statistics and Computing A 189-201. 
  11. HERLIN, I., NGUYEN, C., and GRAFFIGNE, C. ( 1992). Stochastic Segmentation of ultrasound images, in 11th IAPR International Conference on Pattern Recognition, IEEE Computer Society Press, 1 289-292. 
  12. HURN, M. ( 1995). On the use of auxiliary variables in Markov chain Monte-Carlo methods, Tech. Rep. #95-07, Statistics Group at the University of Bath, School of Mathematical Sciences, University of Bath, Bath, BA2 7AY. 
  13. HURN, M. and JENNISON, C. ( 1993). Multiple-site updates in maximum a posteriori and marginal posterior modes image estimation, in Advances in Applied Statistics: Statistics and Images, Mardia and Kanji eds., Oxford - Carfax, 155-186. 
  14. MARTINELLI, F. ( 1992). Dynamical analysis of low-temperature Monte-Carlo cluster algorithms. J. Stat. Physics 66 1245-1276. Zbl0925.82181MR1156404
  15. MARTINELLI, F., OLIVIERI, E., and SCOPPOLA, E. ( 1991). On the Swendsen-Wang dynamics. I. Exponential convergence to equilibrium. J. Stat. Physics 62 117-133. Zbl0739.60097MR1105259
  16. MARTINELLI, F., OLIVIERI, E., and SCOPPOLA, E. ( 1991). On the Swendsen-Wang dynamics. II. Critical droplets and homogeneous nucleation at low temperature for the two-dimensional Ising models. J. Stat. Physics 62 117-133. Zbl0739.60097MR1105259
  17. SOKAL, A. D.( 1989). Monte-Carlo methods in statistical mechanics: Foundations and new algorithms. Cours de troisième cycle de la physique en Suisse Romande, Lausanne. 
  18. SWENDSEN, R. H. and WANG, J. S. ( 1987). Nonuniversal critical dynamics in Monte-Carlo simulation. Physical Review Letters 58 86-88. 
  19. WANG, J. ( 1994). Multiscale Markov fields: applications to the segmentation of textured images and film fusion, PhD thesis, Orsay University. 
  20. WANG, J. ( 1997). Stochastic relaxation on partitions with connected components and its application to image segmentation. Preprint CMLA, Cachan, France. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.