Markov Random Field Approach Research Articles

A Gaussian Markov random field approach to convergence analysis

Spatial models have been widely applied in the context of growth regressions with spatial spillovers usually modelled by simultaneous autoregressions (SAR). Although largely used, such a class of models present some logical difficulties connected with the error behaviour, the lack of identifiability of the model parameters and their substantive interpretation. To overcome these logical pitfalls, in this paper we introduce a new specification of regional growth regressions by applying multivariate Gaussian Markov random fields (GMRFs). We discuss the theoretical properties of the proposed model and show some empirical results on the economic growth pattern of 254 NUTS-2 European regions in the period 1992–2006. We show that the proposed GMRF model is able to capture the complexity of the phenomenon including the possibility of estimating site-specific convergence parameters which may highlight clustering of regions and spatial heterogeneities in the speed of convergence.

A Markov Random Field Approach for Sidescan Sonar Change Detection

One of the main challenges in mine detection using sidescan sonar images is the high density of mine-like objects (MLOs) in a clutter environment. This paper proposes an image change detection technique for bitemporal images which suppresses false alarms efficiently without involving large training data sets. The proposed approach uses the spatial dependence of a stationary object between bitemporal images to eliminate the differences caused by a position error. Bayes theory is then employed to classify the changed and unchanged objects. In particular, the a priori probabilities are formulated by the Markov random field (MRF). The likelihood functions are modeled using the coarseness difference of objects as the test statistics, and the parameters are estimated using the expectation-maximization (EM) method. Real sidescan sonar data are used to validate the proposed method. Results show that the proposed MRF change detection method is robust to the poor quality of object boundaries due to speckle noise, and outperforms the conventional pixel-level change detection methods.

Geometrically inspired MRF for moving object detection from mobile stereo camera

Detecting moving objects from an image sequence is challenging, especially when the camera is moving and the background varies significantly in every frame. In addition, classifying moving objects using only their appearances creates ambiguities in complex scenes. In this sense a Markov random field (MRF) approach is proposed incorporating a stereo vision-based structure-from-motion scheme in order to robustly detect the moving objects from image sequences. In this MRF formulation, the new energy terms of a high-order likelihood and a temporal pairwise potential are added to improve the detection performance further. The performance of the proposed method is demonstrated from publicly available datasets.

3D CLASSIFICATION OF CROSSROADS FROM MULTIPLE AERIAL IMAGES USING MARKOV RANDOM FIELDS

Abstract. The precise classification and reconstruction of crossroads from multiple aerial images is a challenging problem in remote sensing. We apply the Markov Random Fields (MRF) approach to this problem, a probabilistic model that can be used to consider context in classification. A simple appearance-based model is combined with a probabilistic model of the co-occurrence of class label at neighbouring image sites to distinguish up to 14 different classes that are relevant for scenes containing crossroads. The parameters of these models are learnt from training data. We use multiple overlap aerial images to derive a digital surface model (DSM) and a true orthophoto without moving cars. From the DSM and the orthophoto we derive feature vectors that are used in the classification. One of the features is a car confidence value that is supposed to support the classification when the road surface is occluded by static cars. Our approach is evaluated on a dataset of airborne photos of an urban area by a comparison of the results to reference data. Whereas the method has problems in distinguishing classes having a similar appearance, it is shown to produce promising results if a reduced set of classes is considered, yielding an overall classification accuracy of 74.8%.

Automatic Detection of Gadolinium-Enhancing Multiple Sclerosis Lesions in Brain MRI Using Conditional Random Fields

Gadolinium-enhancing lesions in brain magnetic resonance imaging of multiple sclerosis (MS) patients are of great interest since they are markers of disease activity. Identification of gadolinium-enhancing lesions is particularly challenging because the vast majority of enhancing voxels are associated with normal structures, particularly blood vessels. Furthermore, these lesions are typically small and in close proximity to vessels. In this paper, we present an automatic, probabilistic framework for segmentation of gadolinium-enhancing lesions in MS using conditional random fields. Our approach, through the integration of different components, encodes different information such as correspondence between the intensities and tissue labels, patterns in the labels, or patterns in the intensities. The proposed algorithm is evaluated on 80 multimodal clinical datasets acquired from relapsing-remitting MS patients in the context of multicenter clinical trials. The experimental results exhibit a sensitivity of 98% with a low false positive lesion count. The performance of the proposed algorithm is also compared to a logistic regression classifier, a support vector machine and a Markov random field approach. The results demonstrate superior performance of the proposed algorithm at successfully detecting all of the gadolinium-enhancing lesions while maintaining a low false positive lesion count.

GPU-accelerated MRF segmentation algorithm for SAR images

Markov Random Field (MRF) approaches have been widely studied for Synthetic Aperture Radar (SAR) image segmentation, but they have a large computational cost and hence are not widely used in practice. Fortunately parallel algorithms have been documented to enjoy significant speedups when ported to run on a graphics processing units (GPUs) instead of a standard CPU. Presented here is an implementation of graphics processing units in General Purpose Computation (GPGPU) for SAR image segmentation based on the MRF method, using the C-oriented Compute Unified Device Architecture (CUDA) developed by NVIDIA. This experiment with GPGPU shows that the speed of segmentation can be increased by a factor of 10 for large images.

A Markov Random Field Approach for Topology-Preserving Registration: Application to Object-Based Tomographic Image Interpolation

This paper proposes a topology-preserving multiresolution elastic registration method based on a discrete Markov random field of deformations and a block-matching procedure. The method is applied to the object-based interpolation of tomographic slices. For that purpose, the fidelity of a given deformation to the data is established by a block-matching strategy based on intensity- and gradient-related features, the smoothness of the transformation is favored by an appropriate prior on the field, and the deformation is guaranteed to maintain the topology by imposing some hard constraints on the local configurations of the field. The resulting deformation is defined as the maximum a posteriori configuration. Additionally, the relative influence of the fidelity and smoothness terms is weighted by the unsupervised estimation of the field parameters. In order to obtain an unbiased interpolation result, the registration is performed both in the forward and backward directions, and the resulting transformations are combined by using the local information content of the deformation. The method is applied to magnetic resonance and computed tomography acquisitions of the brain and the torso. Quantitative comparisons offer an overall improvement in performance with respect to related works in the literature. Additionally, the application of the interpolation method to cardiac magnetic resonance images has shown that the removal of any of the main components of the algorithm results in a decrease in performance which has proven to be statistically significant.

A prior feature SVM-MRF based method for mouse brain segmentation

We introduce an automated method, called prior feature Support Vector Machine-Markov Random Field (pSVMRF), to segment three-dimensional mouse brain Magnetic Resonance Microscopy (MRM) images. Our earlier work, extended MRF (eMRF) integrated Support Vector Machine (SVM) and Markov Random Field (MRF) approaches, leading to improved segmentation accuracy; however, the computation of eMRF is very expensive, which may limit its performance on segmentation and robustness. In this study pSVMRF reduces training and testing time for SVM, while boosting segmentation performance. Unlike the eMRF approach, where MR intensity information and location priors are linearly combined, pSVMRF combines this information in a nonlinear fashion, and enhances the discriminative ability of the algorithm. We validate the proposed method using MR imaging of unstained and actively stained mouse brain specimens, and compare segmentation accuracy with two existing methods: eMRF and MRF. C57BL/6 mice are used for training and testing, using cross validation. For formalin fixed C57BL/6 specimens, pSVMRF outperforms both eMRF and MRF. The segmentation accuracy for C57BL/6 brains, stained or not, was similar for larger structures like hippocampus and caudate putamen, (~87%), but increased substantially for smaller regions like susbtantia nigra (from 78.36% to 91.55%), and anterior commissure (from ~50% to ~80%). To test segmentation robustness against increased anatomical variability we add two strains, BXD29 and a transgenic mouse model of Alzheimer's disease. Segmentation accuracy for new strains is 80% for hippocampus, and caudate putamen, indicating that pSVMRF is a promising approach for phenotyping mouse models of human brain disorders.

Adaptive Markov Random Field Approach for Classification of Hyperspectral Imagery

An adaptive Markov random field (MRF) approach is proposed for classification of hyperspectral imagery in this letter. The main feature of the proposed method is the introduction of a relative homogeneity index for each pixel and the use of this index to determine an appropriate weighting coefficient for the spatial contribution in the MRF classification. In this way, overcorrection of spatially high variation areas can be avoided. Support vector machines are implemented for improved class modeling and better estimate of spectral contribution to this approach. Experimental results of a synthetic hyperspectral data set and a real hyperspectral image demonstrate that the proposed method works better on both homogeneous regions and class boundaries with improved classification accuracy.

Accuracy assessment of contextual classification results for vegetation mapping

A new procedure for quantitatively assessing the geometric accuracy of thematic maps, obtained from classifying hyperspectral remote sensing data, is presented. More specifically, the methodology is aimed at the comparison between results from any of the currently popular contextual classification strategies. The proposed procedure characterises the shapes of all objects in a classified image by defining an appropriate reference and a new quality measure. The results from the proposed procedure are represented in an intuitive way, by means of an error matrix, analogous to the confusion matrix used in traditional thematic accuracy representation. A suitable application for the methodology is vegetation mapping, where lots of closely related and spatially connected land cover types are to be distinguished. Consequently, the procedure is tested on a heathland vegetation mapping problem, related to Natura 2000 habitat monitoring. Object-based mapping and Markov Random Field classification results are compared, showing that the selected Markov Random Fields approach is more suitable for the fine-scale problem at hand, which is confirmed by the proposed procedure.

Supervised High-Resolution Dual-Polarization SAR Image Classification by Finite Mixtures and Copulas

In this paper, a novel supervised classification approach is proposed for high-resolution dual-polarization (dual-pol) amplitude satellite synthetic aperture radar (SAR) images. A novel probability density function (pdf) model of the dual-pol SAR data is developed that combines finite mixture modeling for marginal probability density functions estimation and copulas for multivariate distribution modeling. The finite mixture modeling is performed via a recently proposed SAR-specific dictionary-based stochastic expectation maximization approach to SAR amplitude pdf estimation. For modeling the joint distribution of dual-pol data the statistical concept of copulas is employed, and a novel dictionary-based copula-selection method method is proposed. In order to take into account the contextual information, the developed joint pdf model is combined with a Markov random field approach for Bayesian image classification. The accuracy of the developed dual-pol supervised classification approach is validated and compared with benchmark approaches on two high-resolution dual-pol TerraSAR-X scenes, acquired during an epidemiological study. A corresponding single-channel version of the classification algorithm is also developed and validated on a single polarization COSMO-SkyMed scene.

Fast Lipid And Water Levels by Extraction with Spatial Smoothing (FLAWLESS): Three‐dimensional volume fat/water separation at 7 Tesla

To quickly and robustly separate fat/water components of 7T MR images in the presence of field inhomogeneity for the study of metabolic disorders in small animals. Starting with a Markov random field (MRF) based formulation for the 3-point Dixon separation problem, we incorporated new implementation strategies, including stability tracking, multiresolution image pyramid, and improved initial value generation. We term the new method FLAWLESS (Fast Lipid And Water Levels by Extraction with Spatial Smoothing). Compared with non-MRF techniques, FLAWLESS decreased the fat-water swapping mistakes in all of the three-dimensional (3D) animal volumes that we tested. FLAWLESS converged in approximately 1/60th of the computation time of other MRF approaches. The initial value generation of FLAWLESS further improved robustness to field inhomogeneity in 3D volume data. We have developed a novel 3-point Dixon technique found to be useful for high field small animal imaging. It is being used to assess lipid depots and metabolic disorders as a function of genes, diet, age, and therapy.

Analytical assessment of intelligent segmentation techniques for cortical tissues of MR brain images: a comparative study

Medical image segmentation is one of the difficult tasks in image processing since the accuracy of segmentation determines the eventual success or failure of proper diagnosis. In medical imaging identification of each pixel in a region has vital importance since it can increase the standard of evaluation criteria. In this respect segmentation of brain MR images has become more significant in research and medical applications related to diagnosis of abnormality and diseases appearing in human brain. Segmentation initiates the process of extraction of various cortical tissues which is a key issue in neuroscience, to detect early neural disorders. The aim of present study is to comprehensively evaluate intensity based fuzzy C-means and Markov random field approaches, both stochastic and deterministic, for the segmentation of brain MR images into three different cortical tissues--gray matter, white matter and cerebrospinal fluid. Along with the analytical assessment of the segmentation techniques including efficiency and user interaction, this work is concentrated on empirical evaluation based on area based matrix. The results illustrate that in all respects, Markov Random field based approaches are showing better performance as compared to fuzzy C-means. Further, the Markov random field approaches are compared to find out which segmentation technique will suit which initial conditions.

Unsupervised Extraction of Flood-Induced Backscatter Changes in SAR Data Using Markov Image Modeling on Irregular Graphs

The near real-time provision of precise information about flood dynamics from synthetic aperture radar (SAR) data is an essential task in disaster management. A novel tile-based parametric thresholding approach under the generalized Gaussian assumption is applied on normalized change index data to automatically solve the three-class change detection problem in large-size images with small class a priori probabilities. The thresholding result is used for the initialization of a hybrid Markov model which integrates scale-dependent and spatiocontextual information into the labeling process by combining hierarchical with noncausal Markov image modeling. Hierarchical maximum a posteriori (HMAP) estimation using the Markov chains in scale, originally developed on quadtrees, is adapted to hierarchical irregular graphs. To reduce the computational effort of the iterative optimization process that is related to noncausal Markov models, a Markov random field (MRF) approach is defined, which is applied on a restricted region of the lowest level of the graph, selected according to the HMAP labeling result. The experiments that were performed on a bitemporal TerraSAR-X StripMap data set from South West England during and after a large-scale flooding in 2007 confirm the effectiveness of the proposed change detection method and show an increased classification accuracy of the hybrid MRF model in comparison to the sole application of the HMAP estimation. Additionally, the impact of the graph structure and the chosen model parameters on the labeling result as well as on the performance is discussed.

Structured learning approach to image descriptor combination

In this study, the authors address the problem of combining descriptors for purposes of object categorisation and classification. The authors cast the problem in a structured learning setting by viewing the classifier bank and the codewords used in the categorisation and classification tasks as random fields. In this manner, the authors can abstract the problem into a graphical model setting, in which the fusion operation is a transformation over the field of descriptors and classifiers. Thus, the problem reduces itself to that of recovering the optimal transformation using a cost function which is convex and can be converted into either a quadratic or linear programme. This cost function is related to the target function used in discrete Markov random field approaches. The authors demonstrate the utility of our algorithm for purposes of image classification and learning class categories on two datasets.

A Conditional Random Field Approach to Unsupervised Texture Image Segmentation

An unsupervised multiresolution conditional random field (CRF) approach to texture segmentation problems is introduced. This approach involves local and long-range information in the CRF neighbourhood to determine the classes of image blocks. Likemost Markov random field (MRF) approaches, the proposed method treats the image as an array of random variables and attempts to assign an optimal class label to each. While most MRFs involve only local information extracted from a small neighbourhood, our method also allows a few long-range blocks to be involved in the labelling process. This alleviates the problem of assigning different class labels to disjoint regions of the same texture and oversegmentation due to the lack of long-range interaction among the neighbouring and distant blocks. The proposed method requires no a priori knowledge of the number and types of regions/textures.

Variational segmentation algorithms with label frequency constraints

We consider image and signal segmentation problems within the Markov random field (MRF) approach and try to take into account label frequency constraints. Incorporating these constraints into MRF leads to an NP-hard optimization problem. For solving this problem we present a two-step approximation scheme that allows one to use hard, interval and soft constraints on label frequencies. On the first step a factorized approximation of the joint distribution is made (only local terms are included) and then, on the second step, the labeling is found by conditional maximization of the factorized joint distribution. The latter task is reduced to an easy-to-solve transportation problem. Basing on the proposed two-step approximation scheme we derive the ELM algorithm for tuning MRF parameters. We show the efficiency of our approach on toy signals and on the task of automated segmentation of Google Maps.

Classification using distance nearest neighbours

This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label should depend more on class labels which are closer in the feature space, than those which are further away. Our approach builds on previous work by Holmes and Adams (2002, 2003) and Cucala et al. (2008). Our work shares many of the advantages of these approaches in providing a probabilistic basis for the statistical inference. In comparison to previous work, we present a more efficient computational algorithm to overcome the intractability of the Markov random field model. The results of our algorithm are encouraging in comparison to the k-nearest neighbour algorithm.

Markov random fields reveal an N-terminal double beta-propeller motif as part of a bacterial hybrid two-component sensor system.

The recent explosion in newly sequenced bacterial genomes is outpacing the capacity of researchers to try to assign functional annotation to all the new proteins. Hence, computational methods that can help predict structural motifs provide increasingly important clues in helping to determine how these proteins might function. We introduce a Markov Random Field approach tailored for recognizing proteins that fold into mainly beta-structural motifs, and apply it to build recognizers for the beta-propeller shapes. As an application, we identify a potential class of hybrid two-component sensor proteins, that we predict contain a double-propeller domain.

Automated brain tumor segmentation using spatial accuracy-weighted hidden Markov Random Field

A variety of algorithms have been proposed for brain tumor segmentation from multi-channel sequences, however, most of them require isotropic or pseudo-isotropic resolution of the MR images. Although co-registration and interpolation of low-resolution sequences, such as T2-weighted images, onto the space of the high-resolution image, such as T1-weighted image, can be performed prior to the segmentation, the results are usually limited by partial volume effects due to interpolation of low-resolution images. To improve the quality of tumor segmentation in clinical applications where low-resolution sequences are commonly used together with high-resolution images, we propose the algorithm based on Spatial accuracy-weighted Hidden Markov random field and Expectation maximization (SHE) approach for both automated tumor and enhanced-tumor segmentation. SHE incorporates the spatial interpolation accuracy of low-resolution images into the optimization procedure of the Hidden Markov Random Field (HMRF) to segment tumor using multi-channel MR images with different resolutions, e.g., high-resolution T1-weighted and low-resolution T2-weighted images. In experiments, we evaluated this algorithm using a set of simulated multi-channel brain MR images with known ground-truth tissue segmentation and also applied it to a dataset of MR images obtained during clinical trials of brain tumor chemotherapy. The results show that more accurate tumor segmentation results can be obtained by comparing with conventional multi-channel segmentation algorithms.