Abstract
Monte Carlo methods and their subsequent simulated annealing are able to minimize general energy functions. However, the slow convergence of simulated annealing compared with more recent deterministic algorithms such as graph cuts and belief propagation hinders its popularity over the large dimensional Markov Random Field (MRF). In this paper, we propose a new efficient sampling-based optimization algorithm called WA (Window Annealing) over squared lattice MRF, in which cluster sampling and annealing concepts are combined together. Unlike the conventional annealing process in which only the temperature variable is scheduled, we design a series of artificial ”guiding” (auxiliary) probability distributions based on the general sequential Monte Carlo framework. These auxiliary distributions lead to the maximum a posteriori (MAP) state by scheduling both the temperature and the proposed maximum size of the windows (rectangular cluster) variable. This new annealing scheme greatly enhances the mixing rate and consequently reduces convergence time. Moreover, by adopting the integral image technique for computation of the proposal probability of a sampled window, we can achieve a dramatic reduction in overall computations. The proposed WA is compared with several existing Monte Carlo based optimization techniques as well as state-of-the-art deterministic methods including Graph Cut (GC) and sequential tree re-weighted belief propagation (TRW-S) in the pairwise MRF stereo problem. The experimental results demonstrate that the proposed WA method is comparable with GC in both speed and obtained energy level.
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Keywords
- Simulated Annealing
- Markov Random Field
- Global Constraint
- Sequential Monte Carlo
- Detailed Balance Condition
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.
References
Sun, J., Zheng, N.N., Shum, H.Y.: Stereo matching using belief propagation. PAMI 25 (2003)
Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. PAMI 23 (2001)
Potetz, B.: Efficient belief propagation for vision using linear constraint nodes. CVPR (2007)
Rother, C., Kolmogorov, V., Minka, T., Blake, A.: Cosegmenation of image pairs by histogram matching- incorporating a global constraint into mrfs. CVPR (2006)
Rother, C., Kolmogorov, V., Lepistsky, V., Szummer, M.: Optimizing binary mrfs via extended roof duality. CVPR (2007)
Kohli, P., Mudigonda, P., Torr, P.: p 3 and beyond: Solving energies with higher order cliques. CVPR (2007)
Lan, X., Roth, S., Huttenlocher, D., Black, M.J.: Efficient belief propagation with learned higher-order markov random fields. In: ECCV (2006)
Barbu, A., Zhu, S.C.: Generalizing swendsen-wang cut to sampling arbitrary posterior probabilities. PAMI 27 (2005)
Geman, S., Geman, D.: Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. PAMI 6 (1984)
Tu, Z., Zhu, S.C.: Image segmentation by data-driven markov chain monte carlo. PAMI 24 (May 2002)
Zhu, S.C., Liu, X.W., Wu, Y.N.: Exploring texture ensembles by efficent markov chain monte carlo: Toward a trichromacy theory of texture. PAMI 22(6) (2000)
Liu, J.S.: Monte carlo strategies in scientific computing. Springer, Heidelberg (2001)
Moral, P.D., Doucet, A., Jasra, A.: Sequential monte carlo for bayesian computation. Bayesian Statics (2006)
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N.: Equations of state calculations by fast computing machines. Journal of Chemical Physics 21 (1953)
Hasting, W.K.: Monte carlo sampling methods using markov chains and their applications. Biometrika 57 (1970)
Kirkpatrick, S., Gelatt, C.D., Vechi, M.P.: Optimization by simulated annealing. Science 220 (1983)
Jasra, A., Stephens, D.A., Holmes, C.C.: On population-based simulation for static inference. Statistics and Computing 17 (2007)
Neal, R.M.: Annealed importance sampling. Technical Report 9805, University of Toronto (1998)
Andrieu, C., Freitas, N., Doucet, A., Jordan, M.: An introduction to mcmc for machine learning. Machine Learning 50 (2003)
Crow, F.: Summed-area tables for texture mapping. SIGGRAPH (1984)
Tappen, M., Freeman, W.: Comparison of graph cuts with belief propagation for stereo, using identical mrf parameters. In: ICCV (2003)
Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M., Rother, C.: A comparative study of energy minimization methods for markov random fields. In: ECCV (2006)
Scharstein, D., Szeliski, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. IJCV (2002)
Scharstein, D., Szeliski, R.: High-accuracy stereo depth maps using structured light. CVPR (2003)
Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts? PAMI 26 (2004)
Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. PAMI 26 (2004)
Wainwright, M.J., Jaakkola, T.S., Willsky, A.S.: Map estimation via agreement on trees: Message-passing and linear-programming approaches. IEEE Trans. Information Theory 51(11) (2005)
Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. PAMI 28 (2006)
Sudderth, E.B., Ihler, A.T., Freeman, W.T., Willsky, A.S.: Nonparametric belief propagation. MIT LIDS Technical Report P-2551 (2002)
Birchfield, S., Tomasi, C.: A pixel dissimilarity measure that is insensiitive to image samplin. PAMI 20 (1998)
Rother, C., Kolmogorov, V., Minka, T., Blake, A.: Cosegmentation of image pairs by histogram matchin- incorporating a global constraint into mrfs. CVPR (2006)
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Jung, H.Y., Lee, K.M., Lee, S.U. (2008). Window Annealing over Square Lattice Markov Random Field. In: Forsyth, D., Torr, P., Zisserman, A. (eds) Computer Vision – ECCV 2008. ECCV 2008. Lecture Notes in Computer Science, vol 5303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88688-4_23
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DOI: https://doi.org/10.1007/978-3-540-88688-4_23
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