Figure. 1
Inference in Markov Random Fields can be cast as the minimization of a potential function that is typically composed of unary and pairwise terms. The pairwise potentials measure the cost of assigning labels to two neighboring pixels and are often in the form of differences between labels, rather than of their separate values. We generalize this formulation to allow pairwise potentials to depend on both label differences AND their separate values. We also show that the minimization can be computed efficiently by using an extended version of the generalized distance transform in the belief propagation algorithm. We show that the generalized potential function may be useful in applications such as image restoration and labeling where fine grained control is desirable.
Geometrically the message passing with the extended pairwise potential is equivalent to computing the lower envelope of a set of parabolas ( or cones ) with unequal eccentricity ( or slope ). This extension ( right in Figure.1 ) generalizes the generalized distance transform ( left in Figure.1 ). Here are the MATLAB/C++ [Code] and the [Paper].
