Hierarchical Markov Random Field Model Research Articles

Inference in cylindrical models having latent Markovian classes—With an application to ocean current data

Spatial direction vector data can be represented cylindrically by linear magnitudes and circular angles. We analyze such data by using a hierarchical Markov random field model with latent discrete classes and conditionally independent cylindrical data given the classes. The structure of a Potts model segments the spatial domain, and each class defines a cylindrical density that represents a specific structure. We consider two types of cylindrical distributions; the Weibull sine-skewed von Mises distribution, which is skewed in the circular part, and the generalized Pareto-type wrapped Cauchy distribution, which is heavy-tailed in the linear part. In this setting, we develop a statistically efficient block composite likelihood method for parameter estimation. The method is shown to provide much faster convergence than an expectation–maximization approach. However, the convergence is less stable for the block composite likelihood method, and we suggest a hybrid estimation approach for practical use. We apply the approach to study ocean surface currents in the Norwegian Sea. The models are able to describe the currents in terms of interpretable local regimes of two–three classes. Scoring rules are used to measure predictive performance of the two cylindrical densities. Results indicate that there is clearly skew angular components, and possibly also some heavy tails in magnitude.

An Object-Based Hierarchical Compound Classification Method for Change Detection in Heterogeneous Optical and SAR Images

Change detection in heterogeneous remote sensing images is an important but challenging task because of the incommensurable appearances of the heterogeneous images. In order to solve the change detection problem in optical and synthetic aperture radar (SAR) images, this paper proposes an improved method that combines cooperative multitemporal segmentation and hierarchical compound classification (CMS-HCC) based on our previous work. Considering the large radiometric and geometric differences between heterogeneous images, first, a cooperative multitemporal segmentation method is introduced to generate multi-scale segmentation results. This method segments two images together by associating the information from the two images and thus reduces the noises and errors caused by area transition and object misalignment, as well as makes the boundaries of detected objects described more accurately. Then, a region-based multitemporal hierarchical Markov random field (RMH-MRF) model is defined to combine spatial, temporal, and multi-level information. With the RMH-MRF model, a hierarchical compound classification method is performed by identifying the optimal configuration of labels with a region-based marginal posterior mode estimation, further improving the change detection accuracy. The changes can be determined if the labels assigned to each pair of parcels are different, obtaining multi-scale change maps. Experimental validation is conducted on several pairs of optical and SAR images. It consists of two parts: comparison on different multitemporal segmentation methods and comparison on different change detection methods. The results show that the proposed method can effectively detect the changes in heterogeneous images, with low false positive and high accuracy.

Automated Brain Region Segmentation for Single Cell Resolution Histological Images Based on Markov Random Field.

The brain consists of massive regions with different functions and the precise delineation of brain region boundaries is important for brain region identification and atlas illustration. In this paper we propose a hierarchical Markov random field (MRF) model for brain region segmentation, where a MRF is applied to the downsampled low-resolution images and the result is used to initialize another MRF for the original high-resolution images. A fractional differential feature and a gray level co-occurrence matrix are extracted as the observed vector for the MRF and a new potential energy function, which can capture the spatial characteristic of brain regions, is proposed as well. A fuzzy entropy criterion is used to fine-tune the boundary from the hierarchical MRF model. We test the model both on synthetic images and real histological mouse brain images. The result suggests that the model can accurately identify target regions and even the whole mouse brain outline as a special case. An interesting observation is that the model cannot only segment regions with different cell density but also can segment regions with similar cell density and different cell morphology texture. Thus this model shows great potential for building the high-resolution 3D brain atlas.

A functional network estimation method of resting-state fMRI using a hierarchical Markov random field

We propose a hierarchical Markov random field model for estimating both group and subject functional networks simultaneously. The model takes into account the within-subject spatial coherence as well as the between-subject consistency of the network label maps. The statistical dependency between group and subject networks acts as a regularization, which helps the network estimation on both layers. We use Gibbs sampling to approximate the posterior density of the network labels and Monte Carlo expectation maximization to estimate the model parameters. We compare our method with two alternative segmentation methods based on K-Means and normalized cuts, using synthetic and real fMRI data. The experimental results show that our proposed model is able to identify both group and subject functional networks with higher accuracy on synthetic data, more robustness, and inter-session consistency on the real data.

Classification of Very High Resolution SAR Images of Urban Areas Using Copulas and Texture in a Hierarchical Markov Random Field Model

This letter addresses the problem of classifying synthetic aperture radar (SAR) images of urban areas by using a supervised Bayesian classification method via a contextual hierarchical approach. We develop a bivariate copula-based statistical model that combines amplitude SAR data and textural information, which is then plugged into a hierarchical Markov random field model. The contribution of this letter is thus the development of a novel hierarchical classification approach that uses a quad-tree model based on wavelet decomposition and an innovative statistical model. The performance of the developed approach is illustrated on a high-resolution satellite SAR image of urban areas.

Supervised SAR Image MPM Segmentation Based on Region-Based Hierarchical Model

This letter presents a novel method of supervised multiresolution segmentation for synthetic aperture radar images. The method uses a region-based half-tree hierarchical Markov random field model for multiresolution segmentation. To form the region-based multilayer model, the watershed algorithm is employed at each resolution level independently. The nodes of a quadtree in the proposed model are defined as regions instead of pixels. The relationship over scale is studied, and the region-based upward and downward maximization of posterior marginal estimations are deduced. The experimental results for the segmentation of homogeneous areas prove the region-based model much better in terms of robustness to speckle and preservation of edges compared to the pixel-based hierarchical model and the Gibbs sampler with the single-resolution model

Stereo video coding based on frame estimation and interpolation

The paper proposes a stereo video coding system. To ensure compatibility with monoscopic transmission, one of the view sequences is coded and transmitted conforming to the MPEG standard, referred to as the reference stream, and the other view stream is referred to as target stream. Only a few frames of the latter are coded and transmitted, while the rest are skipped and reconstructed at the decoder using a novel stereoscopic frame compensation and interpolation technique, termed SFEI BLCF. In disparity estimation, smooth and accurate disparity fields are obtained by using hierarchical Markov random field (MRF) and Gibbs random field (GRF) models. A fast search method is used to improve the precision and computation speed. Coding and decoding results show that, with only 8/spl sim/30% additional bandwidth over a single view bit stream, one can transmit, store, and reconstruct stereoscopic video sequences with reasonably good performance.

Sonar image segmentation using an unsupervised hierarchical MRF model

This paper is concerned with hierarchical Markov random field (MRP) models and their application to sonar image segmentation. We present an original hierarchical segmentation procedure devoted to images given by a high-resolution sonar. The sonar image is segmented into two kinds of regions: shadow (corresponding to a lack of acoustic reverberation behind each object lying on the sea-bed) and sea-bottom reverberation. The proposed unsupervised scheme takes into account the variety of the laws in the distribution mixture of a sonar image, and it estimates both the parameters of noise distributions and the parameters of the Markovian prior. For the estimation step, we use an iterative technique which combines a maximum likelihood approach (for noise model parameters) with a least-squares method (for MRF-based prior). In order to model more precisely the local and global characteristics of image content at different scales, we introduce a hierarchical model involving a pyramidal label field. It combines coarse-to-fine causal interactions with a spatial neighborhood structure. This new method of segmentation, called the scale causal multigrid (SCM) algorithm, has been successfully applied to real sonar images and seems to be well suited to the segmentation of very noisy images. The experiments reported in this paper demonstrate that the discussed method performs better than other hierarchical schemes for sonar image segmentation.

Unsupervised image segmentation using Markov random field models

We present two unsupervised segmentation algorithms based on hierarchical Markov random field models for segmenting both noisy images and textured images. Each algorithm finds the the most likely number of classes, their associated model parameters and generates a corresponding segmentation of the image into these classes. This is achieved according to the maximum a posteriori criterion. To facilitate this, an MCMC algorithm is formulated to allow the direct sampling of all the above parameters from the posterior distribution of the image. To allow the number of classes to be sampled, a reversible jump is incorporated into the Markov Chain. Experimental results are presented showing rapid convergence of the algorithm to accurate solutions.

A Hierarchical Markov Random Field Model and Multitemperature Annealing for Parallel Image Classification

In this paper, we are interested in massively parallel multiscale relaxation algorithms applied to image classification. It is well known that multigrid methods can improve significantly the convergence rate and the quality of the final results of iterative relaxation techniques. First, we present a classical multiscale model which consists of a label pyramid and a whole observation field. The potential functions of coarser grids are derived by simple computations. The optimization problem is first solved at the higher scale by a parallel relaxation algorithm; then the next lower scale is initialized by a projection of the result. Second, we propose a hierarchical Markov random field model based on this classical model. We introduce new interactions between neighbor levels in the pyramid. It can also be seen as a way to incorporate cliques with far apart sites for a reasonable price. This model results in a relaxation algorithm with a new annealing scheme: the multitemperature annealing (MTA) scheme, which consists of associating higher temperatures to higher levels, in order to be less sensitive to local minima at coarser grids. The convergence to the global optimum is proved by a generalization of the annealing theorem of S. Geman and D. Geman (IEEE Trans. Pattern Anal. Mach. Intell.6, 1984, 721–741).

Image classification using spectral and spatial information based on MRF models

A new criterion for classifying multispectral remote sensing images or textured images by using spectral and spatial information is proposed. The images are modeled with a hierarchical Markov Random Field (MRF) model that consists of the observed intensity process and the hidden class label process. The class labels are estimated according to the maximum a posteriori (MAP) criterion, but some reasonable approximations are used to reduce the computational load. A stepwise classification algorithm is derived and is confirmed by simulation and experimental results.

Texture segmentation based on a hierarchical Markov random field model

This paper presents a new texture segmentation technique for both supervised and unsupervised segmentation. The textured images under study are modeled by a proposed hierarchical Markov random field (MRF) model. This model is formed by combining the binomial model for textures and the multi-level logistic model for region distributions. The supervised segmentation is achieved by a new algorithm which can reach the global maxima of the posteriori distribution even if the textures are modeled by an MRF model. For unsupervised segmentation, a new parameter estimation scheme is proposed to estimate the model parameters directly from a given image. The new technique is verified by a variety of textured images, such as synthesized textures, natural textures and aerial images, in both supervised and unsupervised segmentation cases.