On the effects of normalization in adaptive MRF hierarchies

Authors:
Albert Y. C. Chen;Jason J. Corso
Affiliations:
Dept. of Computer Science and Engineering, University at Buffalo, SUNY;Dept. of Computer Science and Engineering, University at Buffalo, SUNY
Venue:
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
Year:
2010

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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.