On the Effects of Normalization in Adaptive MRF Hierarchies

Abstract. In this paper, we analyze the effects of energy normalization in adaptivehierarchy-based energy minimization methods. Adaptive hierarchies provide a nt 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 energynormalizing schemes. Our experiments show that properly normalized energies facilitate better use of the hierarchies during optimization:...

• Type: Journal
• Year: 2010
• Where: COMPIMAGE
• Authors: Albert Y. C. Chen, Jason J. Corso
• Keywords: Adaptivehierarchy-based Energy Minimization, COMPIMAGE 2010, Energy Terms, Hierarchies, Solid Modeling