The Infinite Hidden Markov Random Field Model

Hidden Markov Random Field (HMRF) models are important statistical tools for image segmentation. However, such models cannot automatically determine the number of clusters. In many practical applications, to determine the number of clusters in advance is impossible. The Dirichlet process mixture (DPM) models are nonparametric Bayesian models which can automatically determine the number of clusters for the clustering problem. A new HMRF model which combines the DPM model with Student's t-distribution is proposed in this paper. Compared to the Gaussian distribution, the Student's t-distribution with heavier-tailed can have more applications. This model can automatically determine the appropriate clustering number from the observed data. In addition, an efficient variational Bayesian inference algorithm is derived to the proposed model. Experimental results show that the proposed model outperforms other DPM-based models in image segmentation.

The hidden Markov random field (HMRF) model is an efficient method for image segmentation. However, it may not accurately segment a poorly defined image like Magnetic Resonance (MR) brain image. The HMRF model uses an initial estimation for tissue segmentation of MR brain image. The initial estimation of an input image has a large role to play to obtain a robust HMRF model. In general, a hard clustering method is used for initial estimation. However, it is not an efficient technique for the segmentation of a complex and irregular shape image like MR brain image. The method of clustering acts as a preprocessing step in improving the performance of HMRF. It aims at producing a set of concise data in the segmentation of brain tissues. In this paper, we propose a new approach to HMRF model, which incorporates the fuzzy C-means (FCM) clustering for the initial estimation of the brain image, which is not found in the literature. This results in efficient segmentation of brain tissues. The results are compared with the spatial FCM clustering algorithm and HMRF model with K-means clustering, using different segmentation evaluation indices. It is seen that the results are better than the other methods.

Hidden Markov random field model based brain MR image segmentation using clonal selection algorithm and Markov chain Monte Carlo method

Change detection is an important part of many remote sensing applications. This paper addresses the problem of unsupervised pixel classification into 'Change' and 'No Change' classes based on Hidden Markov Random Field (HMRF) models. HMRF models have long been recognized as a method to enforce spatially coherent class assignment. The optimal classification under these models is usually obtained under the Maximum a Posteriori (MAP) criterion. However, the MAP classification in HMRF models leads in general to problems with exponential complexity, so approximate techniques are needed. In this paper we show that the simple structure of the change detection problem makes that MAP classification can be exactly and efficiently calculated using graph cut techniques. Another problem related to HMRF modelling (and to any change detection technique) is the determination of the parameters or thresholds for classification. This learning problem is solved in our HMRF model by the Expectation Maximization (EM) algorithm. Experimental results obtained on four sets of multispectral remote sensing images confirm the validity of the proposed approach.

In this paper, we present the region based hidden Markov random field model (RBHMRF), which encodes the characteristics of different brain regions into a probabilistic framework for brain MR image segmentation. The recently proposed TV+L1 model is used for region extraction. By utilizing different spatial characteristics in different brain regions, the RMHMRF model performs beyond the current state-of-the-art method, the hidden Markov random field model (HMRF), which uses identical spatial information throughout the whole brain. Experiments on both real and synthetic 3D MR images show that the segmentation result of the proposed method has higher accuracy compared to existing algorithms.

Accurate brain tissue segmentation from magnetic resonance (MR) images plays an important role in both clinical practice and neuroscience research. In this paper, we extend the hidden Markov random field (HMRF) model, and propose a novel model, called Class-K HMRF model, to further improve the segmentation accuracy by incorporating more contextual information during classification. This model simultaneously takes account of spatial dependencies between image pixels and bias field, and hence can overcome the difficulties caused by noise and intensity inhomogeneity. By comparing our algorithm with state-of-the-art approaches, the experimental results demonstrate that the proposed algorithm can produce more accurate and reliable segmentations.

The aim of this study was to implement a Dirichlet process mixture (DPM) model for automatic tumor edge identification on (18)F-fluorodeoxyglucose positron emission tomography ((18)F-FDG PET) images by optimizing the parameters on which the algorithm depends, to validate it experimentally, and to test its robustness. The DPM model belongs to the class of the Bayesian nonparametric models and uses the Dirichlet process prior for flexible nonparametric mixture modeling, without any preliminary choice of the number of mixture components. The DPM algorithm implemented in the statistical software package R was used in this work. The contouring accuracy was evaluated on several image data sets: on an IEC phantom (spherical inserts with diameter in the range 10-37 mm) acquired by a Philips Gemini Big Bore PET-CT scanner, using 9 different target-to-background ratios (TBRs) from 2.5 to 70; on a digital phantom simulating spherical/uniform lesions and tumors, irregular in shape and activity; and on 20 clinical cases (10 lung and 10 esophageal cancer patients). The influence of the DPM parameters on contour generation was studied in two steps. In the first one, only the IEC spheres having diameters of 22 and 37 mm and a sphere of the digital phantom (41.6 mm diameter) were studied by varying the main parameters until the diameter of the spheres was obtained within 0.2% of the true value. In the second step, the results obtained for this training set were applied to the entire data set to determine DPM based volumes of all available lesions. These volumes were compared to those obtained by applying already known algorithms (Gaussian mixture model and gradient-based) and to true values, when available. Only one parameter was found able to significantly influence segmentation accuracy (ANOVA test). This parameter was linearly connected to the uptake variance of the tested region of interest (ROI). In the first step of the study, a calibration curve was determined to automatically generate the optimal parameter from the variance of the ROI. This "calibration curve" was then applied to contour the whole data set. The accuracy (mean discrepancy between DPM model-based contours and reference contours) of volume estimation was below (1 ± 7)% on the whole data set (1 SD). The overlap between true and automatically segmented contours, measured by the Dice similarity coefficient, was 0.93 with a SD of 0.03. The proposed DPM model was able to accurately reproduce known volumes of FDG concentration, with high overlap between segmented and true volumes. For all the analyzed inserts of the IEC phantom, the algorithm proved to be robust to variations in radius and in TBR. The main advantage of this algorithm was that no setting of DPM parameters was required in advance, since the proper setting of the only parameter that could significantly influence the segmentation results was automatically related to the uptake variance of the chosen ROI. Furthermore, the algorithm did not need any preliminary choice of the optimum number of classes to describe the ROIs within PET images and no assumption about the shape of the lesion and the uptake heterogeneity of the tracer was required.

In this article we propose a modification to the HMRF-EM framework applied to image segmentation. To do so, we introduce a new model for the neighborhood energy function of the Hidden Markov Random Fields model based on the Hidden Markov Model formalism. With this new energy model, we aim at (1) avoiding the use of a key parameter chosen empirically on which the results of the current models are heavily relying, (2) proposing an information rich modelisation of neighborhood relationships.

In machine learning and data mining tasks, Clustering is considered to be one of the most important techniques. The same sorts of documents are grouped by performing clustering techniques. Similarity measuring is used to determine transaction relationships. Hierarchical clustering model generates tree structured results. Partitioned based clustering produces the result in grid format. Text documents are unstructured data values with high dimensional attributes. Document clustering group transforms unlabeled text documents into meaningful clusters. In the event of document grouping process, traditional clustering methods require cluster count (K). Clustering accuracy degrades drastically with reference to the unsuitable cluster count. It is observed that document features are automatically partitioned into two groups namely — discriminative words and non-discriminative words. In particular, discriminative words are only useful for grouping documents. The involvement of non-discriminative words confuses the clustering process and leads to poor clustering solution in return. A variation inference algorithm is used to infer the document collection structure and partition of document words simultaneously. Dirichlet Process Mixture (DPM) model is used to partition documents in a way utilizing both the data likelihood and the clustering property of the Dirichlet Process (DP). Dirichlet Process Mixture Model for Feature Extraction (DPMFE) is used to discover the latent cluster structure based on the DPM model and it is performed without involving the number of clusters as input.

Magnetic resonance imaging evaluation of vertebral tumor prediction using hierarchical hidden Markov random field model on Internet of Medical Things (IOMT) platform

Unsupervised outlier detection using random subspace and subsampling ensembles of Dirichlet process mixtures

SummaryDirichlet process mixtures are flexible nonparametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size increases, and more specifically focus on consistency for the unknown number of clusters when the observed data are generated from a finite mixture. Crucially, we consider the situation where a prior is placed on the concentration parameter of the underlying Dirichlet process. Previous findings in the literature suggest that Dirichlet process mixtures are typically not consistent for the number of clusters if the concentration parameter is held fixed and data come from a finite mixture. Here we show that consistency for the number of clusters can be achieved if the concentration parameter is adapted in a fully Bayesian way, as commonly done in practice. Our results are derived for data coming from a class of finite mixtures, with mild assumptions on the prior for the concentration parameter and for a variety of choices of likelihood kernels for the mixture.

Summary In this study, geological prior information is incorporated in the classification of reservoir lithologies using the Markov Random Field (MRF) technique. The prediction of hidden lithologies in seismic data is based on measured observations such as seismic inversion results, which are associated with the latent categorical variables derived from the distribution of Gaussian assumptions. The Hidden Markov Random Field (HMRF) approach can connect similar lithologies laterally (horizontally) while ensure a geologically reasonable stratigraphic (vertical) ordering. It is, therefore, able to exclude randomly appearing lithologies caused by errors in the inversion. In HMRF, the prior information consists of a Gibbs distribution function and transition probability matrices. The Gibbs distribution connects similar lithologies and does not need a geological definition derived from non-case-related information. The transition matrices provide preferential transitions between different lithologies and an estimation of these matrices implicitly depends on the depositional environments and juxtaposition rules between different lithologies.

Dirichlet process mixture models (or mixture of Dirichlet process [MDP]) are Bayesian non‐parametric mixture models that can solve the problem of determining the number of components in mixture models by assuming infinitely many components. We propose a new approach for MDP by using a matrix‐generalized half‐ distribution as a non‐informative prior for the covariance in the base distribution. This new approach aims to improve the performance of MDP in cases where conjugacy constraints cause underperformance of current priors, such as Wishart distribution or inverse‐Wishart. The effectiveness of this approach is demonstrated through simulations and by comparing its performance on the Old Faithful geyser dataset with existing MDP specifications.

We present an object tracking framework that employs Dirichlet Process Mixture Models (DPMMs) in a multiple hypothesis tracker. DPMMs enable joint detection and tracking of an unknown and variable number of objects in a fully automatic fashion without any initial labeling. At each frame, we extract foreground superpixels and cluster them into objects by propagating clusters across consecutive frames. Since no constraint on the number of clusters is required, we can track multiple cluster hypotheses at the same time. By incorporating superpixels and an efficient pruning scheme, we keep the total number of hypotheses low and tractable. We refine object boundaries with Markov random fields and connectivity analysis of the tracked clusters. Finally, we group tracked hypotheses to combine possible parts of an object as one.