35 research outputs found
Maximum Persistency in Energy Minimization
We consider discrete pairwise energy minimization problem (weighted
constraint satisfaction, max-sum labeling) and methods that identify a globally
optimal partial assignment of variables. When finding a complete optimal
assignment is intractable, determining optimal values for a part of variables
is an interesting possibility. Existing methods are based on different
sufficient conditions. We propose a new sufficient condition for partial
optimality which is: (1) verifiable in polynomial time (2) invariant to
reparametrization of the problem and permutation of labels and (3) includes
many existing sufficient conditions as special cases. We pose the problem of
finding the maximum optimal partial assignment identifiable by the new
sufficient condition. A polynomial method is proposed which is guaranteed to
assign same or larger part of variables than several existing approaches. The
core of the method is a specially constructed linear program that identifies
persistent assignments in an arbitrary multi-label setting.Comment: Extended technical report for the CVPR 2014 paper. Update: correction
to the proof of characterization theore
Maximum Persistency via Iterative Relaxed Inference with Graphical Models
We consider the NP-hard problem of MAP-inference for undirected discrete
graphical models. We propose a polynomial time and practically efficient
algorithm for finding a part of its optimal solution. Specifically, our
algorithm marks some labels of the considered graphical model either as (i)
optimal, meaning that they belong to all optimal solutions of the inference
problem; (ii) non-optimal if they provably do not belong to any solution. With
access to an exact solver of a linear programming relaxation to the
MAP-inference problem, our algorithm marks the maximal possible (in a specified
sense) number of labels. We also present a version of the algorithm, which has
access to a suboptimal dual solver only and still can ensure the
(non-)optimality for the marked labels, although the overall number of the
marked labels may decrease. We propose an efficient implementation, which runs
in time comparable to a single run of a suboptimal dual solver. Our method is
well-scalable and shows state-of-the-art results on computational benchmarks
from machine learning and computer vision.Comment: Reworked version, submitted to PAM
A Distributed Mincut/Maxflow Algorithm Combining Path Augmentation and Push-Relabel
We develop a novel distributed algorithm for the minimum cut problem. We
primarily aim at solving large sparse problems. Assuming vertices of the graph
are partitioned into several regions, the algorithm performs path augmentations
inside the regions and updates of the push-relabel style between the regions.
The interaction between regions is considered expensive (regions are loaded
into the memory one-by-one or located on separate machines in a network). The
algorithm works in sweeps - passes over all regions. Let be the set of
vertices incident to inter-region edges of the graph. We present a sequential
and parallel versions of the algorithm which terminate in at most
sweeps. The competing algorithm by Delong and Boykov uses push-relabel updates
inside regions. In the case of a fixed partition we prove that this algorithm
has a tight bound on the number of sweeps, where is the number of
vertices. We tested sequential versions of the algorithms on instances of
maxflow problems in computer vision. Experimentally, the number of sweeps
required by the new algorithm is much lower than for the Delong and Boykov's
variant. Large problems (up to vertices and edges) are
solved using under 1GB of memory in about 10 sweeps.Comment: 40 pages, 15 figure