Markov Random Field Framework Research Articles

A Markov random field model for change points detection

Detecting Change Points (CPs) in data sequences is a challenging problem that arises in a variety of disciplines, including signal processing and time series analysis. While many methods exist for PieceWise Constant (PWC) signals, relatively fewer address PieceWise Linear (PWL) signals due to the challenge of preserving sharp transitions. This paper introduces a Markov Random Field (MRF) model for detecting changes in slope. The number of CPs and their locations are unknown. The proposed method incorporates PWL prior information using MRF framework with an additional boolean variable called Line Process (LP), describing the presence or absence of CPs. The solution is then estimated in the sense of maximum a posteriori. The LP allows us to define a non-convex non-smooth energy function that is algorithmically hard to minimize. To tackle the optimization challenge, we propose an extension of the combinatorial algorithm DPS, initially designed for CP detection in PWC signals. Also, we present a shared memory implementation to enhance computational efficiency. Numerical studies show that the proposed model produces competitive results compared to the state-of-the-art methods. We further evaluate the performance of our method on three real datasets, demonstrating superior and accurate estimates of the underlying trend compared to competing methods.

SAR image classification using deep features and neighborhood heterogeneity confidence refined spatial constraints

ABSTRACT Recently, frameworks fusing the convolutional neural network (CNN) and Markov random field (MRF) models have been successfully used in synthetic aperture radar (SAR) image classification. Over-smoothing of the details and the incapability to eliminate regional-level misclassification are two common drawbacks of these frameworks, which are caused by the use of conventional neighbourhood consistency based spatial constraints. To address these problems, a neighbourhood heterogeneity confidence – Markov random field (NHC-MRF) and CNN-based framework is proposed for SAR image classification. In this framework, an NHC index is constructed in the binary energy function of the NHC-MRF to refine the conventional spatial constraints by adaptively allowing the existence of heterogeneity in the neighbourhood. The NHC index consists of a label coexisting probability term and a top-2 label term, which are constructed based on the outputs of the CNN. By using the label coexisting probability term, the details can be protected by allowing heterogeneity, and the regional-level misclassification can be eliminated by adjusting the impact of the neighbourhoods by using label coexisting probability based weighting. The top-2 label term is used as a correction of the coexisting probability term considering the disturbance of speckle noise. The NHC-MRF is further fused with a CNN by constructing the unary energy term and initial labels based on the outputs of the CNN. The effectiveness and superiority of the proposed framework are experimentally demonstrated using three SAR datasets. The experimental results demonstrate that the superiority of the NHC-MRF is derived from the simultaneous realization of retaining details and eliminating regional-level misclassification.

Spatiotemporal high-resolution prediction and mapping: methodology and application to dengue disease

Dengue disease has become a major public health problem. Accurate and precise identification, prediction and mapping of high-risk areas are crucial elements of an effective and efficient early warning system in countering the spread of dengue disease. In this paper, we present the fusion area-cell spatiotemporal generalized geoadditive-Gaussian Markov random field (FGG-GMRF) framework for joint estimation of an area-cell model, involving temporally varying coefficients, spatially and temporally structured and unstructured random effects, and spatiotemporal interaction of the random effects. The spatiotemporal Gaussian field is applied to determine the unobserved relative risk at cell level. It is transformed to a Gaussian Markov random field using the finite element method and the linear stochastic partial differential equation approach to solve the “big n” problem. Sub-area relative risk estimates are obtained as block averages of the cell outcomes within each sub-area boundary. The FGG-GMRF model is estimated by applying Bayesian Integrated Nested Laplace Approximation. In the application to Bandung city, Indonesia, we combine low-resolution area level (district) spatiotemporal data on population at risk and incidence and high-resolution cell level data on weather variables to obtain predictions of relative risk at subdistrict level. The predicted dengue relative risk at subdistrict level suggests significant fine-scale heterogeneities which are not apparent when examining the area level. The relative risk varies considerably across subdistricts and time, with the latter showing an increase in the period January–July and a decrease in the period August–December.

Markov random field models for vector-based representations of landscapes

In agricultural landscapes the spatial distribution of cultivated and seminatural elements strongly impacts habitat connectivity and species dynamics. To allow for landscape structural analysis and scenario generation, we here develop statistical tools for real landscapes composed of geometric elements, including 2D patches but also 1D linear elements (e.g., hedges). Utilizing the framework of discrete Markov random fields, we design generative stochastic models that combine a multiplex network representation, based on spatial adjacency, with Gibbs energy terms to capture the distribution of landscape descriptors for land-use categories. We implement simulation of agricultural scenarios with parameter-controlled spatial and temporal patterns (e.g., geometry, connectivity, crop rotation), and we demonstrate through simulation that pseudo-likelihood estimation of parameters works well. To study statistical relevance of model components in real landscapes, we discuss model selection and validation, including cross-validated prediction scores. Model validation with a view toward ecologically relevant landscape summaries is achieved by comparing observed and simulated summaries (network metrics but also metrics and appropriately defined variograms using a raster discretization). Models fitted to subregions of the Lower Durance Valley (France) indicate strong deviation from random allocation and realistically capture landscape patterns. In summary, our approach improves the understanding of agroecosystems and enables simulation-based theoretical analysis of how landscape patterns shape biological and ecological processes.

Quantum field-theoretic machine learning

We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the $\phi^{4}$ scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. We illustrate the concepts by minimizing an asymmetric distance between the probability distribution of the $\phi^{4}$ theory and that of target distributions, by quantifying the overlap of statistical ensembles between probability distributions and through reweighting to complex-valued actions with longer-range interactions. Neural network architectures are additionally derived from the $\phi^{4}$ theory which can be viewed as generalizations of conventional neural networks and applications are presented. We conclude by discussing how the proposal opens up a new research avenue, that of developing a mathematical and computational framework of machine learning within quantum field theory.

Image compression based on Gaussian mixture model constrained using Markov random field

We introduce a Gaussian Mixture Model (GMM) constrained by Markov Random Field (MRF) framework for image compression in this paper. The image is predicted using GMM with MRF and the parameters of the GMM are estimated using an adjusted Expectation-Maximization (EM) algorithm. Mixture Model Optimization (MMO) is used in this framework to select the optimal number of distributions and avoid local optimum of EM at the same time. Parameters are encoded using fixed-length bits. A codebook is used to improve the coding efficiency of the covariance parameters. The residual between the original image and the prediction is encoded using High Efficiency Video Coding (HEVC) intra coding. Experimental results show that our method performs better than our previous work, HEVC, JPEG 2000 and Better Portable Graphics (BPG) which is an improved version of HEVC.

A Weighted Spatially Constrained Finite Mixture Model for Image Segmentation

Spatially Constrained Mixture Model (SCMM) is an image segmentation model that works over the framework of maximum a-posteriori and Markov Random Field (MAP-MRF). It developed its own maximization step to be used within this framework. This research has proposed an improvement in the SCMM’s maximization step for segmenting simulated brain Magnetic Resonance Images (MRIs). The improved model is named as the Weighted Spatially Constrained Finite Mixture Model (WSCFMM). To compare the performance of SCMM and WSCFMM, simulated T1-Weighted normal MRIs were segmented. A region of interest (ROI) was extracted from segmented images. The similarity level between the extracted ROI and the ground truth (GT) was found by using the Jaccard and Dice similarity measuring method. According to the Jaccard similarity measuring method, WSCFMM showed an overall improvement of 4.72%, whereas the Dice similarity measuring method provided an overall improvement of 2.65% against the SCMM. Besides, WSCFMM significantly stabilized and reduced the execution time by showing an improvement of 83.71%. The study concludes that WSCFMM is a stable model and performs better as compared to the SCMM in noisy and noise-free environments.

Blending Surface Segmentation and Editing for 3D Models

Recognizing and fitting shape primitives from underlying 3D models are key components of many computer graphics and computer vision applications. Although a vast number of structural recovery methods are available, they usually fail to identify blending surfaces, which corresponds to small transitional regions among relatively large primary patches. To address this issue, we present a novel approach for automatic segmentation and surface fitting with accurate geometric parameters from 3D models, especially mechanical parts. Overall, we formulate the structural segmentation as a Markov random field (MRF) labeling problem. In contrast to existing techniques, we first propose a new clustering algorithm to build superfacets by incorporating 3D local geometric information. This algorithm extracts the general quadric and rolling-ball blending regions, and improves the robustness of further segmentation. Next, we apply a specially designed MRF framework to efficiently partition the original model into different meaningful patches of known surface types by defining the multilabel energy function on the superfacets. Furthermore, we present an iterative optimization algorithm based on skeleton extraction to fit rolling-ball blending patches by recovering the parameters of the rolling center trajectories and ball radius. Experiments on different complex models demonstrate the effectiveness and robustness of the proposed method, and the superiority of our method is also verified through comparisons with state-of-the-art approaches. We further apply our algorithm in applications such as mesh editing by changing the radius of the rolling balls.

Local structure graph models with higher‐order dependence

AbstractLocal structure graph models (LSGMs) describe random graphs and networks as a Markov random field (MRF)—each graph edge has a specified conditional distribution dependent on explicit neighbourhoods of other graph edges. Centred parameterizations of LSGMs allow for direct control and interpretation of parameters for large‐ and small‐scale structures (e.g., marginal means vs. dependence). We extend this parameterization to account for triples of dependent edges and illustrate the importance of centred parameterizations for incorporating covariates and interpreting parameters. Using a MRF framework, common exponential random graph models are also shown to induce conditional distributions without centred parameterizations and thereby have undesirable features. This work attempts to advance graph models through conditional model specifications with modern parameterizations, covariates and higher‐order dependencies.

Iterated graph cut method for automatic and accurate segmentation of finger-vein images

Recent advances in computer vision and machine intelligence have facilitated biometric technologies, which increasingly rely on image data in security practices. As an important biometric identifier, the near-infrared (NIR) finger-vein pattern is favoured by non-contact, high accuracy, and enhanced security systems. However, large stacks of low-contrast and complex finger-vein images present barriers to manual image segmentation, which locates the objects of interest. Although some headway in computer-aided segmentation has been made, state-of-the-art approaches often require user interaction or prior training, which are tedious, time-consuming and prone to operator bias. Recognizing this deficiency, the present study exploits structure-specific contextual clues and proposes an iterated graph cut (IGC) method for automatic and accurate segmentation of finger-vein images. To this end, the geometric structures of the image-acquisition system and the fingers provide the hard (centreline along the finger) and shape (rectangle around the finger) constraints. A node-merging scheme is applied to reduce the computational burden. The Gaussian probability model determines the initial labels. Finally, the maximum a posteriori Markov random field (MAP-MRF) framework is tasked with iteratively updating the data models of the object and the background. Our approach was extensively evaluated on 4 finger-vein databases and compared with some benchmark methods. The experimental results indicate that the proposed IGC method outperforms the state-of-the-practice approaches in finger-vein image segmentation. Specifically, the IGC method, relative to its level set deep learning (LSDL) counterpart, can increase the average F-measure value by 5.03%, 6.56%, 49.91%, and 22.89% when segmenting images from four different finger-vein databases. Therefore, this work can provide a feasible path towards fully automatic image segmentation.

A Software Defined Radio Cross-Layer Resource Allocation Approach for Cognitive Radio Networks: From Theory to Practice

Software Defined Radio (SDR)-enabled cognitive radio network architectures are expected to play an important role in the future 5G networks. Despite the increased research interest, the current implementations are of small-scale and provide limited functionality. In this paper, we contribute towards the alleviation of the limitations in SDR deployments by developing and evaluating a resource allocation approach for cognitive radios implemented with SDR technology over two testbeds of the ORCA federation. Resource allocation is based on a Markov Random Field (MRF) framework realizing a distributed cross-layer computation for the secondary nodes of the cognitive radio network. The proposed framework implementation consists of self-contained modules developed in GNU Radio realizing cognitive functionalities, such as spectrum sensing, collision detection, etc. We demonstrate the feasibility of the MRF based resource allocation approach and provide extensive results and performance analysis that highlight its key features. The latter provide useful insights about the advantages of our framework, while allowing to pinpoint current technological barriers of broader interest.

A network-based integrated framework for predicting virus-prokaryote interactions.

Metagenomic sequencing has greatly enhanced the discovery of viral genomic sequences; however, it remains challenging to identify the host(s) of these new viruses. We developed VirHostMatcher-Net, a flexible, network-based, Markov random field framework for predicting virus–prokaryote interactions using multiple, integrated features: CRISPR sequences and alignment-free similarity measures (n}{}s_2^* and WIsH). Evaluation of this method on a benchmark set of 1462 known virus–prokaryote pairs yielded host prediction accuracy of 59% and 86% at the genus and phylum levels, representing 16–27% and 6–10% improvement, respectively, over previous single-feature prediction approaches. We applied our host prediction tool to crAssphage, a human gut phage, and two metagenomic virus datasets: marine viruses and viral contigs recovered from globally distributed, diverse habitats. Host predictions were frequently consistent with those of previous studies, but more importantly, this new tool made many more confident predictions than previous tools, up to nearly 3-fold more (n > 27 000), greatly expanding the diversity of known virus–host interactions.

Smart Commuter Line (KRL) using IoT and SOA in Indonesia

Commuter line (KRL) one of the better public transportation for commuter people in Indonesia especially in Jabodetabek (Jakarta, Bogor, Depok, Tangerang, Bekasi). Passenger satisfaction is the one of the service quality factor in KRL. There is no real time passenger information in both train and station, the situation make an unpredictable activity for passenger that want to use or wait the commuter line (KRL). Most of passenger cannot enter the train because the crowded passenger. KRL management cannot manage train capacity and train time management to meet passenger needs. This paper proposed a smart commuter line system to provide real time passenger information using IoT by count people using Markov Random Field framework and integrate all KRL enterprise system using SOA to support data integration.

A Bilevel Contextual MRF Model for Supervised Classification of High Spatial Resolution Remote Sensing Images

Markov random field (MRF) based methods have been widely used in high spatial resolution (HSR) image classification. However, many existing MRF-based methods put more emphasis on pixel level contexts while less on superpixel level contextual information. To cope with this issue, this article presents a novel bilevel contextual MRF framework, named BLC-MRF, for HSR imagery classification. Specifically, pixel and superpixel level dependence are incorporated into the proposed MRF model to fully exploit spectral–spatial contextual information and preserve object boundaries in HSR images. In BLC-MRF, a pixel level MRF model is first performed and then cascaded as an input of a superpixel level MRF. In superpixel level, unary and pairwise potential terms are constructed by using the superpixel probability estimation method and spectral histogram distance, respectively. At last, a contextual MRF model is conducted and the final classification map can be computed by using $\alpha$ -expansion algorithm. The benefits of BLC-MRF are twofold: first, the pixel and superpixel level contextual information can be exploited under MRF framework to preserve object boundaries for improving the classification performance, and, second, the algorithm can provide promising results with a small number of training samples. Experimental results on three HSR datasets demonstrate that the proposed approach outperforms several state-of-the-art methods in terms of the classification performance.

Effective piecewise planar modeling based on sparse 3D points and convolutional neural network

Piecewise planar stereo methods can approximately reconstruct the complete structures of a scene by overcoming challenging difficulties (e.g., poorly textured regions) that pixel-level stereo methods cannot resolve. In this paper, a novel plane assignment cost is first constructed by incorporating scene structure priors and high-level image features obtained by convolutional neural network (CNN). Then, the piecewise planar scene structures are reconstructed in a progressive manner that jointly optimizes image regions (or superpixels) and their associated planes, followed by a global plane assignment optimization under a Markov Random Field (MRF) framework. Experimental results on a variety of urban scenes confirm that the proposed method can effectively reconstruct the complete structures of a scene from only sparse three-dimensional (3D) points with high efficiency and accuracy and can achieve superior results compared with state-of-the-art methods.

Data-Independent Feature Learning with Markov Random Fields in Convolutional Neural Networks

In image classification, deriving robust image representations is a key process that determines the performance of vision systems. Numerous image features and descriptors have been developed manually over the years. As an alternative, however, deep neural networks, in particular convolutional neural networks (CNNs), have become popular for learning image features or representations from data and have demonstrated remarkable performance in many real-world applications. But CNNs often require huge amount of labelled data, which may be prohibitive in many applications, as well as long training times. This paper considers an alternative, data-independent means of obtaining features for CNNs. The proposed framework makes use of the Markov random field (MRF) and self-organising map (SOM) to generate basic features and model both intra- and inter-image dependencies. Various MRF textures are synthesized first, and are then clustered by a convolutional translation-invariant SOM, to form generic image features. These features can be directly applied as early convolutional filters of the CNN, leading to a new way of deriving effective features for image classification. The MRF framework also offers a theoretical and transparent way to examine and determine the influence of image features on performance of CNNs. Comprehensive experiments on the MNIST, rotated MNIST, CIFAR-10 and CIFAR-100 datasets were conducted with results outperforming most state-of-the-art models of similar complexity.

Group-representative functional network estimation from multi-subject fMRI data via MRF-based image segmentation

Background and objectiveThere has been growing interest in using functional connectivity patterns, determined from fMRI data to characterize groups of individuals exhibiting common traits. However, the present challenge lies in efficient and accurate identification of distinct patterns observed consistently across multiple subjects. Existing approaches either impose strong assumptions, require aligning images before processing, or require data-intensive machine learning algorithms with manually labeled training datasets. In this paper, we propose a more principled and flexible approach to address this. MethodsOur approach redefines the problem of estimating the group-representative functional network as an image segmentation problem. After employing an improved clustering-based ICA scheme to pre-process the dataset of individual functional network images, we use a maximum a posteriori–Markov random field (MAP-MRF) framework to solve the image segmentation problem. In this framework, we propose a probabilistic model of the individual pixels of the fMRI data, with the model involving a latent group-representative functional network image. Given an observed dataset, we apply a novel and efficient variational Bayes algorithm to recover the associated latent group image. Our methodology seeks to overcome limitations in more traditional schemes by exploiting spatial relationships underlying the connectivity maps and accounting for uncertainty in the estimation process. ResultsWe validate our approach using synthetic, simulated and real data. First, we generate datasets from the proposed forward model with subject-specific binary masking and measurement noise, as well as from a variant of the model without measurement noise. We use both datasets to evaluate our model, along with two algorithms: coordinate-ascent algorithm and variational Bayes algorithm. We conclude that our proposed model with variational Bayes outperforms other competitors, even under model-misspecification. Using variational Bayes offers a significant improvement in performance, with almost no additional computational overhead. We next test our approach on simulated fMRI data. We show our approach is robust to initialization and can recover a solution close to the ground truth. Finally, we apply our proposed methodology along with baselines to a real dataset of fMRI recordings of individuals from two groups, a control group and a group suffering from depression, with recordings made while individuals were subjected to musical stimuli. Our methodology is able to identify group differences that are less clear under competing methods. ConclusionsOur model-based approach demonstrates the advantage of probabilistic models and modern algorithms that account for uncertainty in accurate identification of group-representative connectivity maps. The variational Bayes methodology yields highly accurate results without increasing the computational load compared to traditional methods. In addition, it is robust to model misspecification, and increases the ability to avoid local optima in the solution.

Incorporating Network Embedding into Markov Random Field for Better Community Detection

Recent research on community detection focuses on learning representations of nodes using different network embedding methods, and then feeding them as normal features to clustering algorithms. However, we find that though one may have good results by direct clustering based on such network embedding features, there is ample room for improvement. More seriously, in many real networks, some statisticallysignificant nodes which play pivotal roles are often divided into incorrect communities using network embedding methods. This is because while some distance measures are used to capture the spatial relationship between nodes by embedding, the nodes after mapping to feature vectors are essentially not coupled any more, losing important structural information. To address this problem, we propose a general Markov Random Field (MRF) framework to incorporate coupling in network embedding which allows better detecting network communities. By smartly utilizing properties of MRF, the new framework not only preserves the advantages of network embedding (e.g. low complexity, high parallelizability and applicability for traditional machine learning), but also alleviates its core drawback of inadequate representations of dependencies via making up the missing coupling relationships. Experiments on real networks show that our new approach improves the accuracy of existing embedding methods (e.g. Node2Vec, DeepWalk and MNMF), and corrects most wrongly-divided statistically-significant nodes, which makes network embedding essentially suitable for real community detection applications. The new approach also outperforms other state-of-the-art conventional community detection methods.

A Hybrid Model Integrating Spatial Pattern, Spatial Correlation, and Edge Information for Image Classification

This paper develops a novel hybrid model that integrates three spatial contexts into probabilistic classifiers for remote sensing classification. First, spatial pattern is introduced using multiple-point geostatistics (MPGs) to characterize the general distribution and arrangement of land covers. Second, spatial correlation is incorporated using spatial covariance to quantify the dependence between pixels. Third, an edge-preserving filter based on the Sobel mask is introduced to avoid the over-smoothing problem. These three types of contexts are combined with the spectral information from the original image within a higher-order Markov random field (MRF) framework for classification. The developed model is capable of classifying complex and diverse land cover types by allowing effective anisotropic filtering of the image while retaining details near edges. Experiments with three remote sensing images from different sources based on three probabilistic classifiers obtained results that significantly improved classification accuracies when compared with other popular contextual classifiers and most state-of-the-art methods.

A Markov Random Field Framework for Modeling Malware Propagation in Complex Communications Networks

The proliferation of complex communication networks (CCNs) and their importance for maintaining social coherency nowadays have urgently elevated the need for protecting networking infrastructures from malicious software attacks. In this paper, we propose a Markov Random Field (MRF) based spatio-stochastic framework for modeling the macroscopic behavior of a CCN under random attack, where malicious threats propagate through direct interactions and follow the Susceptible-Infected-Susceptible infection paradigm. We exploit the MRF framework for analytically studying the propagation dynamics in various types of CCNs, i.e., lattice, random, scale-free, small-world and multihop graphs, in a holistic manner. By combining Gibbs sampling with simulated annealing, we study the behavior of the above systems for various topological and malware related parameters with respect to the general random attacks considered. We demonstrate the effectiveness of the MRF framework in capturing the evolution of SIS malware propagation and use it to assess the robustness of synthetic and real CCNs with respect to the involved parameters. It is found that random networks are more robust, followed by scale-free, regular and small-world, while multihop emerge as the most vulnerable of all.