Abstract
In this paper, we analyze the effects of energy normalization in adaptive-hierarchy-based energy minimization methods. Adaptive hierarchies provide a convenient multi-level abstraction of the underlying MRF. They have been shown to both accelerate computation and help avoid local minima. However, the standard recursive way of accumulating energy throughout the hierarchy causes energy terms to grow at different rates. Consequently, the faster-growing term, typically the unary term, dominates the overall energy at coarser level nodes, which hinders larger-scale energy/label change from happening. To solve the problem, we first investigate the theory and construction of adaptive hierarchies, then we analyze the theoretical bounds and expected values of its energy terms. Based on these analyses, we design and experimentally analyze three different energy-normalizing schemes. Our experiments show that properly normalized energies facilitate better use of the hierarchies during optimization: we observe an average improvement in the speed by 15% with the same accuracy.
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References
Ahuja, N.: A transform for multiscale image segmentation by integrated edge and region detection. IEEE Trans. on Pattern Analysis and Machine Intelligence 18(12), 1211–1235 (1996)
Besag, J.: Spatial interaction and the statistical analysis of lattice systems (with discussion). Journal of the Royal Statistical Society, B 36, 192–236 (1974)
Bouman, C., Liu, B.: Multiple resolution segmentation of textured images. IEEE Trans. on Pattern Analysis and Machine Intelligence 13(2), 99–113 (1991)
Bouman, C., Shapiro, M.: A multiscale random field model for Bayesian image segmentation. IEEE Trans. on Image Processing 3(2), 162–177 (1994)
Boykov, Y., Veksler, O., Zabih, R.: Fast Approximate Energy Minimization via Graph Cuts. IEEE Trans. Pattern Analysis and Machine Learning 23(11), 1222–1239 (2001)
Chen, A.Y.C., Corso, J.J., Wang, L.: HOPS: Efficient region labeling using higher order proxy neighborhoods. In: Proc. of International Conference on Pattern Recognition (2008)
Corso, J.J., Yuille, A., Tu, Z.: Graph-Shifts: Natural Image Labeling by Dynamic Hierarchical Computing. In: Proc. of IEEE Conf. on Computer Vision and Pattern Recognition (2008)
Geman, S., Geman, D.: Stochastic Relaxation, Gibbs Distributions, and Bayesian Restoration of Images. IEEE Trans. on Pattern Analysis and Machine Intelligence 6, 721–741 (1984)
Gidas, B.: A renormalization group approach to image processing problems. IEEE Trans. on Pattern Analysis and Machine Intelligence 11(2), 164–180 (1989)
Kato, Z., Berthod, M., Zerubia, J.: Multiscale Markov random field models for parallel imageclassification. In: Proc. of Fourth International Conference on Computer Vision (1993)
Sharon, E., Brandt, A., Basri, R.: Fast Multiscale Image Segmentation. In: Proc. of IEEE Conf. on Computer Vision and Pattern Recognition, vol. I, pp. 70–77 (2000)
Terzopoulos, D.: Image analysis using multigrid relaxation methods. IEEE Trans. on Pattern Analysis and Machine Intelligence 8(2), 129–139 (1986)
Tu, Z.: Probabilistic Boosting-Tree: Learning Discriminative Models for Classification, Recognition, and Clustering. In: Proc. of the Tenth IEEE Int’l Conf. on Computer Vision, vol. 2 (2005)
Yao, Z., Yang, X., Zhu, S.C.: Introduction to a Large Scale General Purpose Ground Truth Dataset: Methodology, Annotation Tool, and Benchmarks. In: Yuille, A.L., Zhu, S.-C., Cremers, D., Wang, Y. (eds.) EMMCVPR 2007. LNCS, vol. 4679, pp. 169–183. Springer, Heidelberg (2007)
Yedidia, J., Freeman, W., Weiss, Y.: Generalized Belief Propagation. Advances in Neural Information Processing Systems 13, 689–695 (2000)
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Chen, A.Y.C., Corso, J.J. (2010). On the Effects of Normalization in Adaptive MRF Hierarchies. In: Barneva, R.P., Brimkov, V.E., Hauptman, H.A., Natal Jorge, R.M., Tavares, J.M.R.S. (eds) Computational Modeling of Objects Represented in Images. CompIMAGE 2010. Lecture Notes in Computer Science, vol 6026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12712-0_25
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DOI: https://doi.org/10.1007/978-3-642-12712-0_25
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