Exact Optimization for Markov Random Fields with Convex Priors

By Hiroshi Ishikawa. 2003

620 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Molecular Biology, Signal Processing

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, background): “What makes DPPs particularly unique is the marriage of these computational advantages with the ability to express global, negative interactions between modeling variables; this repulsive domain is notoriously intractable using traditional approaches like graphical models [17, 70, 82, 109, 146, 156, ”
An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision (2001, methodology): “This work was mainly done while the authors were with Siemens Corp. Research, Princeton, NJ.”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, background): “cuts is used to find an approximate minimum (note that in certain cases where labels are ordered, an exact formulation is possible [105, 55, 97]).”
A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors (2008, background): “If the labels have a linear ordering (for example, consecutive integers) and the smoothness cost is an arbitrary convex function, the work in [24] gives a graphcut construction for an exact solution.”
Total Variation Minimization and a Class of Binary MRF Models (2005, methodology): “been then extended to much more general problems in the recent years [18, 7, 20, 21, 22, 25].”
Computing geodesics and minimal surfaces via graph cuts (2003, background): “One attractive feature of the graph cut approach is that it can find a global minimum of the energy (e.g. [13] [28] [15] [2]).”
A Survey and Comparison of Discrete and Continuous Multi-label Optimization Approaches for the Potts Model (2013, background): “The linear KT-relaxation (Kleinberg and Tardos (2002)), –”
What energy functions can be minimized via graph cuts? (2002, background): “This construction has been further generalized to handle an arbitrary convex V [22].”
Robust Higher Order Potentials for Enforcing Label Consistency (2008, methodology): “The same transformation technique can be used to minimize some functions of multi-valued variables (Flach 2002; Ishikawa 2003; Schlesinger and Flach 2006).”
A convex relaxation approach for computing minimal partitions (2009, background): “Unfortunately, many interesting Computer Vision problems are not covered by the class considered by Ishikawa.”
Graph Cuts and Efficient N-D Image Segmentation (2006, background): “This graph construction was further generalized to handle arbitrary convex interactions in Ishikawa (2003) .”
Minimizing Nonsubmodular Functions with Graph Cuts-A Review (2007, background): “They were introduced into computer vision in the late 1980s [17] and reintroduced in the 1990s [12], [20], [24].”
A Comparative Study of Energy Minimization Methods for Markov Random Fields (2006, background): “If the labels are the integers starting with 0 and the smoothness cost is an arbitrary convex function, [20] gives a graph cut construction.”
Joint motion estimation and segmentation of complex scenes with label costs and occlusion modeling (2012, methodology): “Results are shown on several classical motion segmentation and optical flow examples.”
A Linear Programming Approach to Max-Sum Problem: A Review (2007, background): “[ GPS89]; Ishikawa and Geiger [IG98, Ish03] for the bivariate functions being convex univariate functions of diﬀerences of variable pairs; Cohen et al .”
Stereo correspondence by dynamic programming on a tree (2005, background): “Except for some special cases [18, 13], optimizing the energy function in 1 is NP-hard.”
Simultaneous truth and performance level estimation (STAPLE): an algorithm for the validation of image segmentation (2004, neutral): “A recent extension of this maximum flow-minimum cut strategy removing the restriction to binary labels has been described [43].”
Phase Unwrapping via Graph Cuts (2005, background): “At this point a reference to work [57] should be made: it introduces an energy minimization for convex potentials also by computing a max-flow/min-cut on a certain graph.”
Higher-order clique reduction in binary graph cut (2009, background): “[5]), [10] Second → 1st order [14, 8] → binary (fusion [29]) Higher → 1st order (this paper) → binary (fusion, this paper)”