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Probability Models of Data Generation
Published in Richard M. Golden, Statistical Machine Learning, 2020
Equivalence of Hidden Markov Field and Hidden Markov Model. In Example 10.3.3, a Hidden Markov Model was proposed to specify a probability model for a part-of-speech tagging problem. Construct a Hidden Markov Random Field (HMRF) which has the same joint distribution and the same conditional independence assumptions as the Hidden Markov Model(HMM) in Example 10.3.3 subject to the constraint that the positivity condition holds. In some applications, the Hidden Markov Random Field probabilistic representation may have advantages because it specifies the probability of the current part-of-speech tag, hk, based not only upon the preceding part-of-speech tag, hk−1, but also the subsequent part-of-speech tag hk+1 as well as the observed word wk. However, the HMRF representation may require more computationally intensive sampling methods (see Chapter 11 and Chapter 12) than the HMM representation.
Mixture Models for Image Analysis
Published in Sylvia Frühwirth-Schnatter, Gilles Celeux, Christian P. Robert, Handbook of Mixture Analysis, 2019
In the context of statistical image segmentation, choosing the probabilistic model that best accounts for the observations is an important first step for the quality of the subsequent estimation and analysis. Hidden Markov random field (HMRF) models were revealed to be a powerful tool for image segmentation (Geman & Geman, 1984; Besag, 1986). They are very useful in accounting for spatial dependencies between the different pixels of an image, but these spatial dependencies are also responsible for a typically large amount of computation. Markov model-based segmentation requires estimation of the model parameters. A common approach involves alternately restoring the unknown segmentation (labelling or clustering) based on a maximum a posteriori rule and then estimating the model parameters using the observations and the restored data. This is the case, for instance, in the popular iterated conditional mode (ICM) algorithm of Besag (1986) which makes use of the pseudo-likelihood approximation (Besag, 1974). This combination usually provides reasonable segmentations but is known to lead to biased parameter estimates, essentially due to the restoration step. Because of the missing data structure of the task, the expectation-maximization (EM) algorithm provides another justifiable formalism for such an alternating scheme. It has the advantage of dealing with conditional probabilities instead of committing to suboptimal restorations of the hidden data.
Hidden Markov random field model and Broyden–Fletcher–Goldfarb–Shanno algorithm for brain image segmentation
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2018
EL-Hachemi Guerrout, Samy Ait-Aoudia, Dominique Michelucci, Ramdane Mahiou
This paper presents a new segmentation method referred to as HMRF-BFGS, which combines HMRF (Hidden Markov Random Field) and BFGS (Broyden–Fletcher–Goldfarb–Shanno). The segmentation quality is evaluated using the Dice Coefficient (DC) (Dice, 1945) criterion. This coefficient measures how much the segmentation result is close to the ground truth. Brain MR (Magnetic Resonance) images segmentation has attracted a particular attention in medical imaging. Our tests focus on BrainWeb1 (Cocosco, Kollokian, Kwan, Pike, & Evans, 1997) and IBSR2, widely used databases, where the ground truth is known. This paper is organised as follows. Section 2 presents the hidden Markov field model. The BFGS algorithm is explained in Section 3. The Section 4 is devoted to the experimental results. Finally, Section 5 concludes the paper.
An improved tumor segmentation algorithm from T2 and FLAIR multimodality MRI brain images by support vector machine and genetic algorithm
Published in Cogent Engineering, 2018
Aswathy Sukumaran, Devadhas G. Glan, S. S. Kumar
There exist different methods for the image segmentation and processing Priyanka (2013). These methods can be supervised, semi-supervised, and unsupervised. Zhang, Brady, and Smith (2001) proposed a new method known as Hidden Markov Random Field (HMRF) model. This model has the ability to encode both the spatial and statistical properties of a given image. When compared with existing methods, it is more flexible for image modeling. The limitation of this system is that its preliminary estimations is based on threshold value which is purely heuristic and its time consuming. It gives inaccurate results most of the time. Tolba, Mostafa, Gharib, and Salem (2003) proposed a new method for MRI brain image segmentation known as Gaussian Multi-Resolution Expectation Maximization algorithm. This algorithm is based on EM algorithm and the multi resolution analysis of the given image. The limitation of this technique is that miss-classified pixel is generated when this algorithm is applied to pixel laying in the edges of boundaries. Agarwal and Kumar (2014) introduced a model based on a threshold value that uses level set methods for 3D brain tumor segmentation.
Tweedie hidden Markov random field and the expectation-method of moments and maximisation algorithm for brain MR image segmentation
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2023
Mouna Zitouni, Masmoudi Afif, Mourad Zribi
Markov random fields (MRFs) have been widely used for computer vision problems, such as image segmentation (Yongyue et al.), surface reconstruction (Vaidya and Boyer 2015) and depth inference (Ashutosh et al. 2008). The HMRF-EM framework was first elaborated for brain segmentation MR images (Yongyue et al.). This classical hidden Markov random field (HMRF) model admits the two following hidden Markov random fields which is an unobservable Markov field, and which is an observable Markov random field. The significance of the MRF models (Thierry 2015; Yongyue et al. ; Quan 2012) refers to the spatial information given by the neighbouring sites.