While widely acknowledged as highly effective in computer vision, multi-label MRFs with non-convex priors are difficult to optimize. To tackle this, we introduce an algorithm that iteratively approximates the original energy with an appropriately weighted surrogate energy that is easier to minimize. Our algorithm guarantees that the original energy decreases at each iteration. In particular, we consider the scenario where the global minimizer of the weighted surrogate energy can be obtained by a multi-label graph cut algorithm, and show that our algorithm then lets us handle of large variety of non-convex priors. We demonstrate the benefits of our method over state-of-the-art MRF energy minimization techniques on stereo and inpainting problems.
Over the years, two different types of approximate MRF energy minimization methods have been proposed. The first class of such methods consists of move-making techniques that were inspired by the success of the graph cut algorithm at solving binary problems in computer vision. These techniques include @math -expansion, @math - @math swap @cite_10 and multi-label moves @cite_8 @cite_9 @cite_13 . The core idea of these methods is to reduce the original multi-label problem to a sequence of binary graph cut problems. Each graph cut problem can then be solved either optimally by the max-flow algorithm @cite_4 if the resulting binary energy is submodular, or approximately via a roof dual technique @cite_22 otherwise. The second type of approximate energy minimization methods consists of message passing algorithms, such as belief propagation (BP) @cite_7 , tree-reweighted message passing (TRW) @cite_23 @cite_3 and the dual decomposition-based approach of @cite_15 , which TRW is a special case of.
@cite_4 @cite_22 @cite_7 @cite_8 @cite_10 @cite_9 @cite_3 @cite_23 @cite_15 @cite_13
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Many vision problems have been formulated as energy minimization problems and there have been significant advances in energy minimization algorithms. The most widely-used energy minimization algorithms include graph cuts, belief propagation and tree-reweighted message passing. Although they have obtained good results, they are still unsatisfactory when it comes to more difficult MRF problems such as non-submodular energy functions, highly connected MRFs, and high-order clique potentials. There have also been other approaches, known as stochastic sampling-based algorithms, which include simulated annealing, Markov chain Monte Carlo and population based Markov chain Monte Carlo. They are applicable to any general energy models but they are usually slower than deterministic methods. In this paper, we propose new algorithms which elegantly combine stochastic and deterministic methods. Sampling-based methods are boosted by deterministic methods so that they can rapidly move to lower energy states and easily jump over energy barriers. In different point of view, the sampling-based method prevents deterministic methods from getting stuck at local minima. Consequently, a combination of both approaches substantially increases the quality of the solutions. We present a thorough analysis of the proposed methods in synthetic MRF problems by controlling the hardness of the problems. We also demonstrate experimental results for the photomontage problem which is the most difficult one among the standard MRF benchmark problems. Many computer vision applications rely on the efficient optimization of challenging, so-called non-submodular, binary pairwise MRFs. A promising graph cut based approach for optimizing such MRFs known as "roof duality" was recently introduced into computer vision. We study two methods which extend this approach. First, we discuss an efficient implementation of the "probing" technique introduced recently by (2006). It simplifies the MRF while preserving the global optimum. Our code is 400-700 faster on some graphs than the implementation of the work of (2006). Second, we present a new technique which takes an arbitrary input labeling and tries to improve its energy. We give theoretical characterizations of local minima of this procedure. We applied both techniques to many applications, including image segmentation, new view synthesis, super-resolution, diagram recognition, parameter learning, texture restoration, and image deconvolution. For several applications we see that we are able to find the global minimum very efficiently, and considerably outperform the original roof duality approach. In comparison to existing techniques, such as graph cut, TRW, BP, ICM, and simulated annealing, we nearly always find a lower energy. This paper addresses the problem of exactly inferring the maximum a posteriori solutions of discrete multi-label MRFs or CRFs with higher order cliques. We present a framework to transform special classes of multi-label higher order functions to submodular second order Boolean functions (referred to as Fs 2), which can be minimized exactly using graph cuts and we characterize those classes. The basic idea is to use two or more Boolean variables to encode the states of a single multi-label variable. There are many ways in which this can be done and much interesting research lies in finding ways which are optimal or minimal in some sense. We study the space of possible encodings and find the ones that can transform the most general class of functions to Fs 2. Our main contributions are two-fold. First, we extend the subclass of submodular energy functions that can be minimized exactly using graph cuts. Second, we show how higher order potentials can be used to improve single view 3D reconstruction results. We believe that our work on exact minimization of higher order energy functions will lead to similar improvements in solutions of other labelling problems. Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper, we focus on the recent technique proposed by (Nov. 2005)- tree-reweighted max-product message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy. However, the algorithm is not guaranteed to increase this bound - it may actually go down. In addition, TRW does not always converge. We develop a modification of this algorithm which we call sequential tree-reweighted message passing. Its main property is that the bound is guaranteed not to decrease. We also give a weak tree agreement condition which characterizes local maxima of the bound with respect to TRW algorithms. We prove that our algorithm has a limit point that achieves weak tree agreement. Finally, we show that, our algorithm requires half as much memory as traditional message passing approaches. Experimental results demonstrate that on certain synthetic and real problems, our algorithm outperforms both the ordinary belief propagation and tree-reweighted algorithm in (M. J. Wainwright, et al, Nov. 2005). In addition, on stereo problems with Potts interactions, we obtain a lower energy than graph cuts