Open Access
Primal-dual Algorithm for Convex Markov Random Fields
V Kolmogorov
- pp 17
TLDR
This paper considers a subclass of minimization problems in which unary and pairwise terms of the energy function are convex, which arise in many vision applications including image restoration, total variation minimization, phase unwrapping in SAR images and panoramic image stitching.Abstract:
Computing maximum a posteriori configuration in a first-order Markov Random Field has become a routinely used approach in computer vision. It is equivalent to minimizing an energy function of discrete variables. In this paper we consider a subclass of minimization problems in which unary and pairwise terms of the energy function are convex. Such problems arise in many vision applications including image restoration, total variation minimization, phase unwrapping in SAR images and panoramic image stitching. We give a new algorithm for computing an exact solution. Its complexity is K · T(n,m) where K is the number of labels and T(n,m) is the time needed to compute a maximum flow in a graph with n nodes and m edges. This is the fastest maxflow-based algorithm for this problem: previously best known technique takes T(nK,mK2) time for general convex functions. Our approach also needs much less memory (O(n+m) instead of O(nK+mK2)). Experimental results show for the panoramic stitching problem our method outperforms other techniques.read more
Citations
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Journal ArticleDOI
Phase Unwrapping via Graph Cuts
TL;DR: A new energy minimization framework for phase unwrapping with considered objective functions are first-order Markov random fields and two algorithms, which solve integer optimization problems by computing a sequence of binary optimizations, each one solved by graph cut techniques are named.
Journal ArticleDOI
A Linear Programming Approach to Max-Sum Problem: A Review
TL;DR: This work reviews a not widely known approach to the max-sum labeling problem, developed by Ukrainian researchers Schlesinger et al. in 1976, and shows how it contributes to recent results, most importantly, those on the convex combination of trees and tree-reweighted max-product.
Book ChapterDOI
Phase unwrapping via graph cuts
TL;DR: A new energy minimization framework for phase unwrapping, where the considered objective functions are first-order Markov random fields, and two algorithms, which solve integer optimization problems by computing a sequence of binary optimizations, each one solved by graph cut techniques are named.
Proceedings ArticleDOI
Graph Cut Based Optimization for MRFs with Truncated Convex Priors
TL;DR: This work develops several optimization algorithms for truncated convex priors, which imply piecewise smoothness assumption, and develops new "range" moves which act on a larger set of labels than the expansion and swap algorithms.
Journal ArticleDOI
SAR Image Regularization With Fast Approximate Discrete Minimization
TL;DR: It is shown that a satisfying solution can be reached by performing a graph-cut-based combinatorial exploration of large trial moves to joint regularization of the amplitude and interferometric phase in urban area SAR images.
References
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