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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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Journal ArticleDOI
TL;DR: In this paper, a statistical approach to aggregate speed and phase (directional) information for vascular segmentation of phase contrast magnetic resonance angiograms (PC-MRA) is presented.

49 citations

Book ChapterDOI
25 Aug 2008
TL;DR: It is proved that the problem of reconstructing bounded-degree models with hidden nodes is hard, and it is impossible to decide in randomized polynomial time if two models generate distributions whose statistical distance is at most 1/3 or at least 2/3.
Abstract: Markov random fields are often used to model high dimensional distributions in a number of applied areas. A number of recent papers have studied the problem of reconstructing a dependency graph of bounded degree from independent samples from the Markov random field. These results require observing samples of the distribution at all nodes of the graph. It was heuristically recognized that the problem of reconstructing the model where there are hidden variables (some of the variables are not observed) is much harder. Here we prove that the problem of reconstructing bounded-degree models with hidden nodes is hard. Specifically, we show that unless NP = RP, It is impossible to decide in randomized polynomial time if two models generate distributions whose statistical distance is at most 1/3 or at least 2/3. Given two generating models whose statistical distance is promised to be at least 1/3, and oracle access to independent samples from one of the models, it is impossible to decide in randomized polynomial time which of the two samples is consistent with the model. The second problem remains hard even if the samples are generated efficiently, albeit under a stronger assumption.

49 citations

Proceedings ArticleDOI
22 Apr 2002
TL;DR: A new electronic colon cleansing technology is presented, which employs a hidden Markov random filed (MRF) model to integrate the neighborhood information for overcoming the non-uniformity problems within the tagged stool/fluid region.
Abstract: Virtual colonoscopy provides a safe, minimal-invasive approach to detect colonic polyps using medical imaging and computer graphics technologies. Residual stool and fluid are problematic for optimal viewing of the colonic mucosa. Electronic cleansing techniques combining bowel preparation, oral contrast agents, and image segmentation were developed to extract the colon lumen from computed tomography (CT) images of the colon. In this paper, we present a new electronic colon cleansing technology, which employs a hidden Markov random filed (MRF) model to integrate the neighborhood information for overcoming the non-uniformity problems within the tagged stool/fluid region. Prior to obtaining CT images, the patient undergoes a bowel preparation. A statistical method for maximum a posterior probability (MAP) was developed to identify the enhanced regions of residual stool/fluid. The method utilizes a hidden MRF Gibbs model to integrate the spatial information into the Expectation Maximization (EM) model-fitting MAP algorithm. The algorithm estimates the model parameters and segments the voxels iteratively in an interleaved manner, converging to a solution where the model parameters and voxel labels are stabilized within a specified criterion. Experimental results are promising.

49 citations

Proceedings ArticleDOI
01 Dec 2013
TL;DR: The trajectory co saliency measure is proposed, which captures the notion that trajectories recurring in all the videos should have their mutual saliency boosted and is formulated as a binary labeling of a Markov Random Field.
Abstract: Given a pair of videos having a common action, our goal is to simultaneously segment this pair of videos to extract this common action. As a preprocessing step, we first remove background trajectories by a motion-based figure ground segmentation. To remove the remaining background and those extraneous actions, we propose the trajectory co saliency measure, which captures the notion that trajectories recurring in all the videos should have their mutual saliency boosted. This requires a trajectory matching process which can compare trajectories with different lengths and not necessarily spatiotemporally aligned, and yet be discriminative enough despite significant intra-class variation in the common action. We further leverage the graph matching to enforce geometric coherence between regions so as to reduce feature ambiguity and matching errors. Finally, to classify the trajectories into common action and action outliers, we formulate the problem as a binary labeling of a Markov Random Field, in which the data term is measured by the trajectory co-saliency and the smoothness term is measured by the spatiotemporal consistency between trajectories. To evaluate the performance of our framework, we introduce a dataset containing clips that have animal actions as well as human actions. Experimental results show that the proposed method performs well in common action extraction.

49 citations

Book ChapterDOI
12 Oct 2008
TL;DR: This work presents a technique for learning the parameters of a continuous-state Markov random field model of optical flow, by minimizing the training loss for a set of ground-truth images using simultaneous perturbation stochastic approximation (SPSA).
Abstract: We present a technique for learning the parameters of a continuous-state Markov random field (MRF) model of optical flow, by minimizing the training loss for a set of ground-truth images using simultaneous perturbation stochastic approximation (SPSA). The use of SPSA to directly minimize the training loss offers several advantages over most previous work on learning MRF models for low-level vision, which instead seek to maximize the likelihood of the data given the model parameters. In particular, our approach explicitly optimizes the error criterion used to evaluate the quality of the flow field, naturally handles missing data values in the ground truth, and does not require the kinds of approximations that current methods use to address the intractable nature of maximum-likelihood estimation for such problems. We show that our method achieves state-of-the-art results and requires only a very small number of training images. We also find that our method generalizes well to unseen data, including data with quite different characteristics than the training set.

48 citations


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