Semi-metric labeling is a special case of energy minimization for pairwise Markov random fields. The energy function consists of arbitrary unary potentials, and pairwise potentials that are proportional to a given sem...
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Semi-metric labeling is a special case of energy minimization for pairwise Markov random fields. The energy function consists of arbitrary unary potentials, and pairwise potentials that are proportional to a given semi-metric distance function over the label set. Popular methods for solving semi-metric labeling include (i) move-making algorithms, which iteratively solve a minimum st-cut problem;and (ii) the linear programming (LP) relaxation based approach. In order to convert the fractional solution of the LP relaxation to an integer solution, several randomized rounding procedures have been developed in the literature. We consider a large class of parallel rounding procedures, and design move-making algorithms that closely mimic them. We prove that the multiplicative bound of a move-making algorithm exactly matches the approximation factor of the corresponding rounding procedure for any arbitrary distance function. Our analysis includes all known results for move-making algorithms as special cases.
Recently, unsupervised image segmentation has become increasingly popular. Starting from a superpixel segmentation, an edge-weighted region adjacency graph is constructed. Amongst all segmentations of the graph, the o...
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ISBN:
(纸本)9781479951178
Recently, unsupervised image segmentation has become increasingly popular. Starting from a superpixel segmentation, an edge-weighted region adjacency graph is constructed. Amongst all segmentations of the graph, the one which best conforms to the given image evidence, as measured by the sum of cut edge weights, is chosen. Since this problem is NP-hard, we propose a new approximate solver based on the move-making paradigm: first, the graph is recursively partitioned into small regions (cut phase). Then, for any two adjacent regions, we consider alternative cuts of these two regions defining possible moves (glue & cut phase). For planar problems, the optimal move can be found, whereas for non-planar problems, efficient approximations exist. We evaluate our algorithm on published and new benchmark datasets, which we make available here. The proposed algorithm finds segmentations that, as measured by a loss function, are as close to the ground-truth as the global optimum found by exact solvers. It does so significantly faster then existing approximate methods, which is important for large-scale problems.
Semi-metric labeling is a special case of energy minimization for pairwise Markov random fields. The energy function consists of arbitrary unary potentials, and pairwise potentials that are proportional to a given sem...
详细信息
Semi-metric labeling is a special case of energy minimization for pairwise Markov random fields. The energy function consists of arbitrary unary potentials, and pairwise potentials that are proportional to a given semi-metric distance function over the label set. Popular methods for solving semi-metric labeling include (i) move-making algorithms, which iteratively solve a minimum st-cut problem; and (ii) the linear programming (LP) relaxation based approach. In order to convert the fractional solution of the LP relaxation to an integer solution, several randomized rounding procedures have been developed in the literature. We consider a large class of parallel rounding procedures, and design move-making algorithms that closely mimic them. We prove that the multiplicative bound of a move-making algorithm exactly matches the approximation factor of the corresponding rounding procedure for any arbitrary distance function. Our analysis includes all known results for move-making algorithms as special cases.
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