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## 1. Clique Reduction by Excludable Local Configuration software (a C++ source code)Version 1.04 (September 12th, 2014.)Download: ELC1.04.zip
Software (a C++ source code) for minimizing a higher-order function of binary variables
E(x_{1}, ..., x_{n}, ..., x_{m}) = Σ_{i} E_{i}(x_{i}) + Σ_{i,j} E_{ij}(x_{i}, x_{j}),possibly with additional variables. Once the function is reduced, minimization itself can be done with known first-order methods, such as the QPBO (roof dual) algorithm below. In this software, there are two ways to reduce a higher-order monomial to first order (second degree). ## A) Finding Excludable Local Configuration (ELC)Reduces the monomial without adding any variable. For some monomials, it cannot be done. So the B) below must be used after A). The technique is described in the following paper:[1] Hiroshi Ishikawa. “Additionally, this software provides an approximation that always reduces the term without additional variables. It does so correctly most of the time, but there is no guarantee. It is much faster, though. This is also described in [1]. ## B) Higher-Order Clique Reduction (HOCR)Additional variables are added to reduce the order of the energy. The number of variables increases exponentially as the order of the given energy increases. The technique is described in the following papers:[2] Hiroshi Ishikawa. “ A demo program that loads the noise-added image and denoise it with a third-order FoE prior is included. This software is implemented so that it can be used most conveniently in combination with the QPBO software by Vladimir Kolmogorov available at his page.
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## 2. Higher-Order Clique Reduction software (a C++ source code)
Download: HOCR1.02a.zip
Software (a C++ source code) for minimizing a higher-order function of binary variables
E(x_{1}, ..., x_{n}, ..., x_{m}) = Σ_{i} E_{i}(x_{i}) + Σ_{i,j} E_{ij}(x_{i}, x_{j}),
on which algorithms such as QPBO and BP can be used.
The additional binary variables The technique in this software is described in the following papers: Hiroshi Ishikawa. “ A demo program that loads the noise-added image and denoise it with a third-order FoE prior is included. This software is implemented so that it can be used most conveniently in combination with the QPBO software by Vladimir Kolmogorov available at his page.
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