bottleneck potentials which penalize the maximum (instead of the sum) over

local potential value taken by the MRF-assignment. Bottleneck potentials or

analogous constructions have been considered in (i) combinatorial optimization

(e.g. bottleneck shortest path problem, the minimum bottleneck spanning tree

problem, bottleneck function minimization in greedoids), (ii) inverse problems

with $L_{\\infty}$-norm regularization, and (iii) valued constraint satisfaction

on the $(\\min,\\max)$-pre-semirings. Bottleneck potentials for general discrete

MRFs are a natural generalization of the above direction of modeling work to

Maximum-A-Posteriori (MAP) inference in MRFs. To this end, we propose MRFs

whose objective consists of two parts: terms that factorize according to (i)

$(\\min,+)$, i.e. potentials as in plain MRFs, and (ii) $(\\min,\\max)$, i.e.

bottleneck potentials. To solve the ensuing inference problem, we propose

high-quality relaxations and efficient algorithms for solving them. We

empirically show efficacy of our approach on large scale seismic horizon

tracking problems.

},\n}\n'