Markov Random Field is now ubiquitous in many formulations
of various vision problems. Recently, optimization
of higher-order potentials became practical using higherorder
graph cuts: the combination of i) the fusion move
algorithm, ii) the reduction of higher-order binary energy
minimization to first-order, and iii) the QPBO algorithm. In
the fusion move, it is crucial for the success and efficiency
of the optimization to provide proposals that fits the energies
being optimized. For higher-order energies, it is even
more so because they have richer class of null potentials.
In this paper, we focus on the efficiency of the higher-order
graph cuts and present a simple technique for generating
proposal labelings that makes the algorithm much more efficient,
which we empirically show using examples in stereo
and image denoising.