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Label assignment problems with large state spaces are important tasksespecially in computer vision. Often the pairwise interaction (or smoothnessprior) between labels assigned at adjacent nodes (or pixels) can be describedas a function of the label difference. Exact inference in such labeling tasksis still difficult, and therefore approximate inference methods based on alinear programming (LP) relaxation are commonly used in practice. In this workwe study how compact linear programs can be constructed for general piecwiselinear smoothness priors. The number of unknowns is O(LK) per pairwise cliquein terms of the state space size $L$ and the number of linear segments K. Thiscompares to an O(L^2) size complexity of the standard LP relaxation if thepiecewise linear structure is ignored. Our compact construction and thestandard LP relaxation are equivalent and lead to the same (approximate) labelassignment.

Compact Relaxations for MAP Inference in Pairwise MRFs with Piecewise Linear Priors