Abstract
Simulated annealing has been applied to a wide variety of problems in image processing and synthesis. However, particularly in scientific applications, the computational complexity of annealing may constrain its effectiveness, in that the demand for very high resolution samples or even three-dimensional data may result in huge configuration spaces. In this paper a method of hierarchical simulated annealing is introduced, which can lead to large gains in computational complexity for suitable models. As an example, the approach is applied to the synthesis of binary porous media images.
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Besag, J., Green, P., Higdon, D., Mengersen, K.: Bayesian computation and stochastic systems (with discussion). Statistical Science 10, 3–66 (1995)
Bouman, C., Shapiro, M.: A multiscale random field model for Bayesian image segmentation. IEEE Image Processing 3(2), 162–177 (1994)
Bouman, C., Liu, B.: Multiple resolution segmentation of textured images. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(2), 99–113 (1991)
Bramble, J.: Multigrid method. John Wiley & Sons, Chichester (1993)
Brémaud, P.: Markov chains: Gibbs fields, monte carlo simulation, and queues. Springer, Heidelberg (1998)
Geiger, D., Kogler Jr., J.E.: Scaling images and image features via the renormalization group. In: Proceedings IEEE CVPR 1993, New York (June 1993)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721–741 (1984)
Gidas, B.: Nonstationary markov chains and convergence of the annealing algorithm. Journal of Statistical Physics 39, 73–131 (1985)
Gidas, B.: A renormalization group approach to image processing problems. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(2), 164–180 (1989)
Hackbusch, W.: Multigrid methods and applications. In: Computational Mathematics, vol. 4. Springer, Heidelberg (1985)
Heitz, F., Perez, P., Bouthemy, P.: Multiscale minimization of global energy functions in some visual recovery problems. Computer Vision, Graphics, and Image Processing. Image Understanding 59(1), 125–134 (1994)
Kato, Z., Berthod, M., Zerubia, J.: A hierarchical Markov random field model and multitemperature annealing for parallel image classification. Graphical Models and Image Processing 58(1), 18–37 (1996)
Liang, Z., Ioannidis, M.A., Chatzis, I.: Reconstruction of 3d porous media using simulated annealing. In: Bentley, et al. (eds.) Computational Methods in Water Resources XIII. Balkema, Rotterdam (2000)
Luettgen, M., Karl, W., Willsky, A., Tenney, R.: Multiscale representations of Markov random fields. IEEE Transactions on Signal Processing 41(12), 3377–3395 (1993)
McCormick, S.: Multigrid methods. SIAM, Philadelphia (1987)
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. Journal of Chemical Physics 21, 1087–1092 (1953)
Paget, R., Longstaff, I.D.: Texture synthesis via a noncausal nonparametric multiscale markov random field. IEEE Transactions on Image Processing 7(6), 925–931 (1998)
Puzicha, J., Buhmann, J.M.: Multiscale annealing for grouping and unsupervised texture segmentation. Computer Vision and Image Understanding: CVIU 76(3), 213–230 (1999)
Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic geometry and its applications, 2nd edn. J. Wiley, Chichester (1996)
Stoyan, D., Stoyan, H.: Fractals, random shapes and point fields: Methods of geometrical statistics. J. Wiley, Chichester (1994)
Swendson, R.H., Wang, J.S.: Nonuniversal critical dynamics in monte carlo simulations. Physical Review Letters 58, 86–88 (1987)
Szu, H., Hartley, R.: Fast simulated annealing. Physics Letters A 122, 157–162 (1987)
Talukdar, M.S., Torsaeter, O., Ionnidis, M.A.: Stochastic recontruction of particulate media from two-dimensional images. Journal of Colloid and Interface Science 248, 419–428 (2002)
Wilson, K., Kogut, J.: The renormalization group and the ε-expansion. Phys. Rep. C12, 75–200 (1974)
Zerubia, J., Kato, Z., Berthod, M.: Multi-temperature annealing: a new approach for the energy-minimization of hierarchical markov random field models. In: Proceedings of the 12th IAPR International Conference on Pattern Recognition, Jerusalem, Israel, vol. 1 (1994)
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Alexander, S.K., Fieguth, P., Vrscay, E.R. (2003). Hierarchical Annealing for Random Image Synthesis. In: Rangarajan, A., Figueiredo, M., Zerubia, J. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2003. Lecture Notes in Computer Science, vol 2683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45063-4_13
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DOI: https://doi.org/10.1007/978-3-540-45063-4_13
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