Adaptive Simulated Annealing for Energy Minimization Problem in a Marked Point Process Application

  • Guillaume Perrin
  • Xavier Descombes
  • Josiane Zerubia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)


We use marked point processes to detect an unknown number of trees from high resolution aerial images. This is in fact an energy minimization problem, where the energy contains a prior term which takes into account the geometrical properties of the objects, and a data term to match these objects to the image. This stochastic process is simulated via a Reversible Jump Markov Chain Monte Carlo procedure, which embeds a Simulated Annealing scheme to extract the best configuration of objects.

We compare here different cooling schedules of the Simulated Annealing algorithm which could provide some good minimization in a short time. We also study some adaptive proposition kernels.


Simulated Annealing Critical Zone Acceptance Ratio Cooling Schedule Marked Point Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Andrieu, C., Breyer, L.A., Doucet, A.: Convergence of Simulated Annealing using Foster-Lyapunov Criteria. Journal of Applied Probability 38(4), 975–994 (2001)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Azencott, R. (ed.): Simulated Annealing. Parallelization Techniques. John Wiley and Sons, Chichester (1992)zbMATHGoogle Scholar
  3. 3.
    Baddeley, A., Van Lieshout, M.N.M.: Stochastic Geometry Models in High-level Vision. In: Mardia, K.V. (ed.) Statistics and Images, vol. 1, pp. 231–256 (1993)Google Scholar
  4. 4.
    Boese, K.D., Kahng, A.B.: Best-so-far vs Where-you-are: Implications for Optimal Finite Time Annealing. System and Control Letters 22, 71–78 (1994)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Cerny, V.: Thermodynamical Approach to the Traveling Salesman Problem: an Efficient Simulation Algorithm. Journal of Optimization Theory and Applications 45(1), 41–51 (1985)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Descombes, X., Kruggel, F., Lacoste, C., Ortner, M., Perrin, G., Zerubia, J.: Marked Point Process in Image Analysis: from Context to Geometry. In: SPPA Conference, Castellon, Spain (April 2004) (invited paper)Google Scholar
  7. 7.
    Fachat, A.: A Comparison of Random Walks with Different Types of Acceptance Probabilities. PhD thesis, University of Chemnitz, Germany (May 2000)Google Scholar
  8. 8.
    Gelfand, S.B., Mitter, S.K.: Metropolis-type Annealing Algorithms for Global Optimization in R d. SIAM Journal of Control and Optimization 31(1), 111–131 (1993)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Geman, S., Geman, D.: Stochastic Relaxation, Gibbs Distributions and Bayesian Restoration of Images. IEEE PAMI 6, 721–741 (1984)zbMATHGoogle Scholar
  10. 10.
    Geyer, C.J., Moller, J.: Likelihood Inference for Spatial Point Processes. In: Barndoff Nielsen, O.E., Kendall, W.S., van Lieshout, M.N.M. (eds.) Stochastic Geometry, Likelihood and Computation. Chapmann and Hall, London (1998)Google Scholar
  11. 11.
    Gougeon, F.A.: Automatic Individual Tree Crown Delineation using a Valley-following Algorithm and Rule-based System. In: Hill, D.A., Leckie, D.G. (eds.) Proc. of the International Forum on Automated Interpretation of High Spatial Resolution Digital Imagery for Forestry, Victoria, British Columbia, Canada, February 1998, pp. 11–23 (1998)Google Scholar
  12. 12.
    Green, P.J.: Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika 82, 711–732 (1995)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Haario, H., Saksman, E.: Simulated Annealing Process in General State Space. Advances Applied Probability 23, 866–893 (1991)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Hajek, B.: Cooling Schedules for Optimal Annealing. Mathematics of Operations Research 13(2), 311–329 (1985)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Halmos, P.R.: Measure Theory. Springer, Heidelberg (1950)zbMATHGoogle Scholar
  16. 16.
    Ingber, L.: Adaptive Simulated Annealing: Lessons Learned. Control and Cybernetics 25(1), 33–54 (1996)zbMATHGoogle Scholar
  17. 17.
    Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science 4598, 220, 671–680 (1983)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Larsen, M.: Individual Tree Top Position Estimation by Template Voting. In: Proc. of the Fourth International Airborne Remote Sensing Conference and Exhibition / 21st Canadian Symposium on Remote Sensing, Ottawa, Ontario, June 1999, vol. 2, pp. 83–90 (1999)Google Scholar
  19. 19.
    Locatelli, M.: Simulated Annealing Algorithms for Continuous Global Optimization: Convergence Conditions. Journal of Optimization Theory and Applications 104, 121–133 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Ortner, M.: Processus Ponctuels Marqués pour l’Extraction Automatique de Caricatures de Bâtiments à partir de Modèles Numériques d’Élévation. PhD thesis, University of Nice-Sophia Antipolis, France (October 2004) (in French)Google Scholar
  21. 21.
    Ortner, M., Descombes, X., Zerubia, J.: A Reversible Jump MCMC Sampler for Object Detection in Image Processing. In: MC2QMC Conference, Antibes Juan Les Pins, France. LNS-Springer, Heidelberg (2004)Google Scholar
  22. 22.
    Perrin, G., Descombes, X., Zerubia, J.: Point Processes in Forestry: an Application to Tree Crown Detection. Research Report 5544, INRIA (April 2005)Google Scholar
  23. 23.
    Salamon, P., Sibani, P., Frost, R.: Facts, Conjectures, and Improvements for Simulated Annealing. In: SIAM Monographs on Mathematical Modeling and Computation. Society for Industrial and Applied Mathematics, Philadelphia (2002)Google Scholar
  24. 24.
    Stoica, R., Gregori, P., Mateu, J.: Simulated Annealing and Object Point Processes: Tools for Analysis of Spatial Patterns. Technical Report 69, University Jaume I, Castellon, Spain (2004)Google Scholar
  25. 25.
    Strenski, P.N., Kirkpatrick, S.: Analysis of Finite Length Annealing Schedules. Algorithmica 6, 346–366 (1991)zbMATHMathSciNetCrossRefGoogle Scholar
  26. 26.
    Szu, H., Hartley, R.: Fast Simulated Annealing. Physics Letters A 122(3-4), 157–162 (1987)CrossRefGoogle Scholar
  27. 27.
    Tafelmayer, R., Hoffmann, K.H.: Scaling Features in Complex Optimization Problems. Computer Physics Communications 86, 81–90 (1995)zbMATHCrossRefGoogle Scholar
  28. 28.
    Tu, Z.W., Zhu, S.C.: Image Segmentation by Data-Driven Markov Chain Monte Carlo. IEEE PAMI 24(5) (2002)Google Scholar
  29. 29.
    van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated Annealing: Theory and Applications. D. Reidel, Boston (1987)zbMATHGoogle Scholar
  30. 30.
    van Lieshout, M.N.M.: Stochastic Annealing for Nearest Neighbour Point Process with Application to Object Recognition. Technical Report BS-R9306, Centruum vor Wiskunde en Informatica, Amsterdam (1993)Google Scholar
  31. 31.
    van Lieshout, M.N.M.: Markov Point Processes and their Applications. Imperial College Press, London (2000)zbMATHCrossRefGoogle Scholar
  32. 32.
    Varanelli, J.M.: On the Acceleration of Simulated Annealing. PhD thesis, University of Virginia, Charlottesville, USA (May 1996)Google Scholar
  33. 33.
    White, S.R.: Concepts of Scale in Simulated Annealing. In: IEEE Proc. of the 1984 International Conference on Computer Design, pp. 646–651 (1984)Google Scholar
  34. 34.
    Winkler, G.: Image Analysis, Random Fields and Markov Chain Monte Carlo Methods, 2nd edn. Springer, Heidelberg (2003)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Guillaume Perrin
    • 1
    • 2
  • Xavier Descombes
    • 2
  • Josiane Zerubia
    • 2
  1. 1.Mas LaboratoryEcole Centrale ParisChatenay-MalabryFrance
  2. 2.Ariana, joint research group INRIA/I3SINRIA Sophia AntipolisSophia Antipolis CedexFrance

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