Higher-order clique reduction in binary graph cut

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Optical flow modeling and computation: A survey (2015, background): “Dealing with higher-order local interactions between pixels has also been addressed in several recent works [86,128,144,150].”
3D Scene Flow Estimation with a Piecewise Rigid Scene Model (2015, background): “Over the years several reduction techniques havebeenproposed(e.g.,Ali et al. 2008; Ishikawa 2009; Rother et al. 2009).”
Harmony Potentials (2011, background): “Other authors use high-order cliques in the original connectivity pattern, and then convert them into order two cliques by the introduction of new variables (Ramalingam et al, 2008; Rother et al, 2009; Ishikawa, 2009; Kohli and Kumar, 2010).”
Multimodal Surface Matching with Higher-Order Smoothness Constraints☆ (2017, methodology): “This allows reduction of higher order terms either by: A) addition of auxiliary variables (for example by reducing a triplet to three pairwise terms (Ishikawa, 2009); or B) by reconfiguration of the polynomial form of the MRF energy, until the higher-order function can be replaced by a single…”