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Markov random field

About: Markov random field is a research topic. Over the lifetime, 5669 publications have been published within this topic receiving 179568 citations. The topic is also known as: MRF.


Papers
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V Kolmogorov1
01 Sep 2005
TL;DR: 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.

40 citations

Book ChapterDOI
03 Sep 2001
TL;DR: This model uses hierarchical Markov random field (HMRF) to segregate overlapping objects into depth layers, and suggests a broader view that clique potentials in MRF models can be used to encode any local decision rules.
Abstract: To segregate overlapping objects into depth layers requires the integration of local occlusion cues distributed over the entire image into a global percept. We propose to model this process using hierarchical Markov random field (HMRF), and suggest a broader view that clique potentials in MRF models can be used to encode any local decision rules. A topology-dependent multiscale hierarchy is used to introduce long range interaction. The operations within each level are identical across the hierarchy. The clique parameters that encode the relative importance of these decision rules are estimated using an optimization technique called learning from rehearsals based on 2-object training samples. We find that this model generalizes successfully to 5-object test images, and that depth segregation can be completed within two traversals across the hierarchy. This computational framework therefore provides an interesting platform for us to investigate the interaction of local decision rules and global representations, as well as to reason about the rationales underlying some of recent psychological and neurophysiological findings related to figure-ground segregation.

40 citations

Journal ArticleDOI
TL;DR: Methods for approximately computing the marginal probability mass functions and means of a Markov random field (MRF) by approximating the lattice by a tree and several theoretical results concerning fixed-point problems are proven.
Abstract: Methods for approximately computing the marginal probability mass functions and means of a Markov random field (MRF) by approximating the lattice by a tree are described. Applied to the a posteriori MRF these methods solve Bayesian spatial pattern classification and image restoration problems. The methods are described, several theoretical results concerning fixed-point problems are proven, and four numerical examples are presented, including comparison with optimal estimators and the iterated conditional mode estimator and including two agricultural optical remote sensing problems. >

40 citations

Proceedings ArticleDOI
16 May 2011
TL;DR: This work shows how to train non-associative Markov networks in a principled manner using the structured Support Vector Machine (SVM) formalism and uses the kernel trick which makes this method one of the first non-linear methods for max-margin Markov Random Field training applied to 3D point cloud segmentation.
Abstract: We address the problem of object class segmentation of 3D point clouds. Each point of a cloud should be assigned a class label determined by the category of the object it belongs to. Non-associative Markov networks have been applied to this task recently. Indeed, they impose more flexible constraints on segmentation results in contrast to the associative ones. We show how to train non-associative Markov networks in a principled manner using the structured Support Vector Machine (SVM) formalism. In contrast to prior work we use the kernel trick which makes our method one of the first non-linear methods for max-margin Markov Random Field training applied to 3D point cloud segmentation. We evaluate our method on airborne and terrestrial laser scans. In comparison to the other non-linear training techniques our method shows higher accuracy.

40 citations

Journal ArticleDOI
TL;DR: It is found that, at least from examples used in the paper, when the distribution function is incorporated with the MRF model to implement SAR image segmentation, the Gamma-MRF model is not necessarily shown to be superior to the Gaussian-MRf model.
Abstract: This paper compares segmentation results of synthetic aperture radar (SAR) images using Gaussian-Markov random field (MRF) and Gamma-MRF models. A Gamma distribution function is more accurate and proper to trace the multilook SAR intensity data distribution. However, it is found that, at least from examples used in the paper, when the distribution function is incorporated with the MRF model to implement SAR image segmentation, the Gamma-MRF model is not necessarily shown to be superior to the Gaussian-MRF model. Occasionally the Gamma-MRF model wrongly merges a few small segments, suggesting that the Gaussian-MRF model might be more stable and reliable.

40 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
202330
2022128
202196
2020173
2019204