3 research outputs found
Combinatorial persistency criteria for multicut and max-cut
In combinatorial optimization, partial variable assignments are called
persistent if they agree with some optimal solution. We propose persistency
criteria for the multicut and max-cut problem as well as fast combinatorial
routines to verify them. The criteria that we derive are based on mappings that
improve feasible multicuts, respectively cuts. Our elementary criteria can be
checked enumeratively. The more advanced ones rely on fast algorithms for upper
and lower bounds for the respective cut problems and max-flow techniques for
auxiliary min-cut problems. Our methods can be used as a preprocessing
technique for reducing problem sizes or for computing partial optimality
guarantees for solutions output by heuristic solvers. We show the efficacy of
our methods on instances of both problems from computer vision, biomedical
image analysis and statistical physics
A Generalized Framework for Agglomerative Clustering of Signed Graphs applied to Instance Segmentation
We propose a novel theoretical framework that generalizes algorithms for
hierarchical agglomerative clustering to weighted graphs with both attractive
and repulsive interactions between the nodes. This framework defines GASP, a
Generalized Algorithm for Signed graph Partitioning, and allows us to explore
many combinations of different linkage criteria and cannot-link constraints. We
prove the equivalence of existing clustering methods to some of those
combinations, and introduce new algorithms for combinations which have not been
studied. An extensive comparison is performed to evaluate properties of the
clustering algorithms in the context of instance segmentation in images,
including robustness to noise and efficiency. We show how one of the new
algorithms proposed in our framework outperforms all previously known
agglomerative methods for signed graphs, both on the competitive CREMI 2016 EM
segmentation benchmark and on the CityScapes dataset.Comment: 19 pages, 8 figures, 6 table