Variational segmentation algorithms with label frequency constraints

Authors:
D. Kropotov;D. Laptev;A. Osokin;D. Vetrov
Affiliations:
Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow, Russia 119333;CMC Department, Lomonosov Moscow State University, Moscow, Russia 119992;CMC Department, Lomonosov Moscow State University, Moscow, Russia 119992;CMC Department, Lomonosov Moscow State University, Moscow, Russia 119992
Venue:
Pattern Recognition and Image Analysis
Year:
2010

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Abstract

We consider image and signal segmentation problems within the Markov random field (MRF) approach and try to take into account label frequency constraints. Incorporating these constraints into MRF leads to an NP-hard optimization problem. For solving this problem we present a two-step approximation scheme that allows one to use hard, interval and soft constraints on label frequencies. On the first step a factorized approximation of the joint distribution is made (only local terms are included) and then, on the second step, the labeling is found by conditional maximization of the factorized joint distribution. The latter task is reduced to an easy-to-solve transportation problem. Basing on the proposed two-step approximation scheme we derive the ELM algorithm for tuning MRF parameters. We show the efficiency of our approach on toy signals and on the task of automated segmentation of Google Maps.