Dynamic Programming for Approximate Expansion Algorithm

Expansion algorithm is a popular optimization method for labeling problems. For many common energies, each expansion step can be optimally solved with a min-cut/max flow algorithm. While the observed performance of max-flow for the expansion algorithm is fast, its theoretical time complexity is worse than linear in the number of pixels. Recently, Dynamic Programming (DP) was shown to be useful for 2D labeling problems via a “tiered labeling” algorithm, although the structure of allowed (tiered) is quite restrictive. We show another use of DP in a 2D labeling case. Namely, we use DP for an approximate expansion step. Our expansion-like moves are more limited in the structure than the max-flow expansion moves. In fact, our moves are more restrictive than the tiered labeling structure, but their complexity is linear in the number of pixels, making them extremely efficient in practice. We illustrate the performance of our DP-expansion on the Potts energy, but our algorithm can be used for any pairwise energies. We achieve better efficiency with almost the same energy compared to the max-flow expansion moves.