An alternative to the alpha-expansion algorithm is the alpha-beta swap. Here, a multilabel MRF with non-convex potentials is optimized by repeatedly choosing pairs of labels α, β and performing a...

An alternative to the alpha-expansion algorithm is the alpha-beta swap. Here, a multilabel MRF with non-convex potentials is optimized by repeatedly choosing pairs of labels

α,




β



and performing a binary graph cut that allows them to swap in such a way that the overall cost function decreases. Devise a graph structure that can be used to perform this operation.

Hint

: consider separate cases for neighboring labels (

α,




α

), (

β,




β

), (

β,




γ

), (

α,




γ

) and (

γ,




γ

) where

γ



is a label that is neither

α

nor

β

.