Graph cuts-based algorithms have achieved great success in energy minimization for many computer vision applications. These algorithms provide approximated solutions for multi-label energy functions via move-making approach. This approach fuses the current solution with a proposal to generate a lower-energy solution. Thus, generating the appropriate proposals is necessary for the success of the move-making approach. However, not much research efforts has been done on the generation of "good" proposals, especially for non-metric energy functions. In this paper, we propose an application-independent and energy-based approach to generate "good" proposals. With these proposals, we present a graph cuts-based move-making algorithm called GA-fusion (fusion with graph approximation-based proposals). Extensive experiments support that our proposal generation is effective across different classes of energy functions. The proposed algorithm outperforms others both on real and synthetic problems.
Some other approaches generate proposals in runtime (, ). Contrary to , the number of the proposals is not limited since they dynamically generate proposals online. @cite_27 , proposals are generated by blurring the current solution and random labeling for denoising application. However, they do not explicitly concern objective energy in proposal generation. And, they are also application-specific. Recently, Ishikawa @cite_6 proposed an application-independent method to generate proposals. This method uses gradient descent algorithm on the objective energy function. Although they are energy-aware and can be applied to some cases, it is still limited to differentiable energy functions. Thus, this method cannot be applied even to the Potts model, which is one of the most popular prior models. In our understanding, this algorithm is only meaningful for ordered labels that represent physical quantities.
@cite_27 @cite_6
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We introduce a new technique that can reduce any higher-order Markov random field with binary labels into a first-order one that has the same minima as the original. Moreover, we combine the reduction with the fusion-move and QPBO algorithms to optimize higher-order multi-label problems. While many vision problems today are formulated as energy minimization problems, they have mostly been limited to using first-order energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higher-order interactions. Our algorithm challenges this restriction that limits the representational power of the models, so that higher-order energies can be used to capture the rich statistics of natural scenes. To demonstrate the algorithm, we minimize a third-order energy, which allows clique potentials with up to four pixels, in an image restoration problem. The problem uses the fields of experts model, a learned spatial prior of natural images that has been used to test two belief propagation algorithms capable of optimizing higher-order energies. The results show that the algorithm exceeds the BP algorithms in both optimization performance and speed. Markov Random Field is now ubiquitous in many formulations of various vision problems. Recently, optimization of higher-order potentials became practical using higher-order graph cuts: the combination of i) the fusion move algorithm, ii) the reduction of higher-order binary energy minimization to first-order, and iii) the QPBO algorithm. In the fusion move, it is crucial for the success and efficiency of the optimization to provide proposals that fits the energies being optimized. For higher-order energies, it is even more so because they have richer class of null potentials. In this paper, we focus on the efficiency of the higher-order graph cuts and present a simple technique for generating proposal labelings that makes the algorithm much more efficient, which we empirically show using examples in stereo and image denoising.