  Label assignment problems with large state spaces are important tasks
especially in computer vision. Often the pairwise interaction (or smoothness
prior) between labels assigned at adjacent nodes (or pixels) can be described
as a function of the label difference. Exact inference in such labeling tasks
is still difficult, and therefore approximate inference methods based on a
linear programming (LP) relaxation are commonly used in practice. In this work
we study how compact linear programs can be constructed for general piecwise
linear smoothness priors. The number of unknowns is O(LK) per pairwise clique
in terms of the state space size $L$ and the number of linear segments K. This
compares to an O(L^2) size complexity of the standard LP relaxation if the
piecewise linear structure is ignored. Our compact construction and the
standard LP relaxation are equivalent and lead to the same (approximate) label
assignment.
