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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: This paper introduces a new supervised segmentation algorithm for remotely sensed hyperspectral image data which integrates the spectral and spatial information in a Bayesian framework and represents an innovative contribution in the literature.
Abstract: This paper introduces a new supervised segmentation algorithm for remotely sensed hyperspectral image data which integrates the spectral and spatial information in a Bayesian framework. A multinomial logistic regression (MLR) algorithm is first used to learn the posterior probability distributions from the spectral information, using a subspace projection method to better characterize noise and highly mixed pixels. Then, contextual information is included using a multilevel logistic Markov-Gibbs Markov random field prior. Finally, a maximum a posteriori segmentation is efficiently computed by the min-cut-based integer optimization algorithm. The proposed segmentation approach is experimentally evaluated using both simulated and real hyperspectral data sets, exhibiting state-of-the-art performance when compared with recently introduced hyperspectral image classification methods. The integration of subspace projection methods with the MLR algorithm, combined with the use of spatial-contextual information, represents an innovative contribution in the literature. This approach is shown to provide accurate characterization of hyperspectral imagery in both the spectral and the spatial domain.

678 citations

Journal ArticleDOI
TL;DR: The proposed scheme for segmentation is based on the iterative conditional modes (ICM) algorithm in which measurement model parameters are estimated using local information at each site, and the prior model parametersare estimated using the segmentation after each cycle of iterations.
Abstract: A statistical model is presented that represents the distributions of major tissue classes in single-channel magnetic resonance (MR) cerebral images. Using the model, cerebral images are segmented into gray matter, white matter, and cerebrospinal fluid (CSF). The model accounts for random noise, magnetic field inhomogeneities, and biological variations of the tissues. Intensity measurements are modeled by a finite Gaussian mixture. Smoothness and piecewise contiguous nature of the tissue regions are modeled by a three-dimensional (3-D) Markov random field (MRF). A segmentation algorithm, based on the statistical model, approximately finds the maximum a posteriori (MAP) estimation of the segmentation and estimates the model parameters from the image data. The proposed scheme for segmentation is based on the iterative conditional modes (ICM) algorithm in which measurement model parameters are estimated using local information at each site, and the prior model parameters are estimated using the segmentation after each cycle of iterations. Application of the algorithm to a sample of clinical MR brain scans, comparisons of the algorithm with other statistical methods, and a validation study with a phantom are presented. The algorithm constitutes a significant step toward a complete data driven unsupervised approach to segmentation of MR images in the presence of the random noise and intensity inhomogeneities.

659 citations

Journal ArticleDOI
TL;DR: The DDMCMC paradigm provides a unifying framework in which the role of many existing segmentation algorithms are revealed as either realizing Markov chain dynamics or computing importance proposal probabilities and generalizes these segmentation methods in a principled way.
Abstract: This paper presents a computational paradigm called Data-Driven Markov Chain Monte Carlo (DDMCMC) for image segmentation in the Bayesian statistical framework. The paper contributes to image segmentation in four aspects. First, it designs efficient and well-balanced Markov Chain dynamics to explore the complex solution space and, thus, achieves a nearly global optimal solution independent of initial segmentations. Second, it presents a mathematical principle and a K-adventurers algorithm for computing multiple distinct solutions from the Markov chain sequence and, thus, it incorporates intrinsic ambiguities in image segmentation. Third, it utilizes data-driven (bottom-up) techniques, such as clustering and edge detection, to compute importance proposal probabilities, which drive the Markov chain dynamics and achieve tremendous speedup in comparison to the traditional jump-diffusion methods. Fourth, the DDMCMC paradigm provides a unifying framework in which the role of many existing segmentation algorithms, such as, edge detection, clustering, region growing, split-merge, snake/balloon, and region competition, are revealed as either realizing Markov chain dynamics or computing importance proposal probabilities. Thus, the DDMCMC paradigm combines and generalizes these segmentation methods in a principled way. The DDMCMC paradigm adopts seven parametric and nonparametric image models for intensity and color at various regions. We test the DDMCMC paradigm extensively on both color and gray-level images and some results are reported in this paper.

638 citations

Book ChapterDOI
05 Sep 2010
TL;DR: This paper presents a simple and effective nonparametric approach to the problem of image parsing, or labeling image regions (in this case, superpixels produced by bottom-up segmentation) with their categories, and establishes a new benchmark for the problem.
Abstract: This paper presents a simple and effective nonparametric approach to the problem of image parsing, or labeling image regions (in our case, superpixels produced by bottom-up segmentation) with their categories. This approach requires no training, and it can easily scale to datasets with tens of thousands of images and hundreds of labels. It works by scene-level matching with global image descriptors, followed by superpixel-level matching with local features and efficient Markov random field (MRF) optimization for incorporating neighborhood context. Our MRF setup can also compute a simultaneous labeling of image regions into semantic classes (e.g., tree, building, car) and geometric classes (sky, vertical, ground). Our system outperforms the state-of-the-art non-parametric method based on SIFT Flow on a dataset of 2,688 images and 33 labels. In addition, we report per-pixel rates on a larger dataset of 15,150 images and 170 labels. To our knowledge, this is the first complete evaluation of image parsing on a dataset of this size, and it establishes a new benchmark for the problem.

606 citations

Journal ArticleDOI
TL;DR: A method to solve exactly a first order Markov random field optimization problem in more generality than was previously possible is introduced, which maps the problem into a minimum-cut problem for a directed graph, for which a globally optimal solution can be found in polynomial time.
Abstract: We introduce a method to solve exactly a first order Markov random field optimization problem in more generality than was previously possible. The MRF has a prior term that is convex in terms of a linearly ordered label set. The method maps the problem into a minimum-cut problem for a directed graph, for which a globally optimal solution can be found in polynomial time. The convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method.

602 citations


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