Markov Random Field Model Research Articles

A formal goodness-of-fit test for spatial binary Markov random field models.

Binary spatial observations arise in environmental and ecological studies, where Markov random field (MRF) models are often applied. Despite the prevalence and the long history of MRF models for spatial binary data, appropriate model diagnostics have remained an unresolved issue in practice. A complicating factor is that such models involve neighborhood specifications, which are difficult to assess for binary data. To address this, we propose a formal goodness-of-fit (GOF) test for diagnosing an MRF model for spatial binary values. The test statistic involves a type of conditional Moran's I based on the fitted conditional probabilities, which can detect departures in model form, including neighborhood structure. Numerical studies show that the GOF test can perform well in detecting deviations from a null model, with a focus on neighborhoods as a difficult issue. We illustrate the spatial test with an application to Besag's historical endive data as well as the breeding pattern of grasshopper sparrows across Iowa.

Statistical batch-aware embedded integration, dimension reduction, and alignment for spatial transcriptomics.

Spatial transcriptomics (ST) technologies provide richer insights into the molecular characteristics of cells by simultaneously measuring gene expression profiles and their relative locations. However, each slice can only contain limited biological variation, and since there are almost always non-negligible batch effects across different slices, integrating numerous slices to account for batch effects and locations is not straightforward. Performing multi-slice integration, dimensionality reduction, and other downstream analyses separately often results in suboptimal embeddings for technical artifacts and biological variations. Joint modeling integrating these steps can enhance our understanding of the complex interplay between technical artifacts and biological signals, leading to more accurate and insightful results. In this context, we propose a hierarchical hidden Markov random field model STADIA to reduce batch effects, extract common biological patterns across multiple ST slices, and simultaneously identify spatial domains. We demonstrate the effectiveness of STADIA using five datasets from different species (human and mouse), various organs (brain, skin, and liver), and diverse platforms (10x Visium, ST, and Slice-seqV2). STADIA can capture common tissue structures across multiple slices and preserve slice-specific biological signals. In addition, STADIA outperforms the other three competing methods (PRECAST, fastMNN, and Harmony) in terms of the balance between batch mixing and spatial domain identification, and it demonstrates the advantage of joint modeling when compared to STAGATE and GraphST. The source code implemented by R is available at https://github.com/zhanglabtools/STADIA and archived with version 1.01 on Zenodo https://zenodo.org/records/13637744.

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.

Adaptive Gaussian Markov random fields for child mortality estimation.

The under-5 mortality rate (U5MR), a critical health indicator, is typically estimated from household surveys in lower and middle income countries. Spatio-temporal disaggregation of household survey data can lead to highly variable estimates of U5MR, necessitating the usage of smoothing models which borrow information across space and time. The assumptions of common smoothing models may be unrealistic when certain time periods or regions are expected to have shocks in mortality relative to their neighbors, which can lead to oversmoothing of U5MR estimates. In this paper, we develop a spatial and temporal smoothing approach based on Gaussian Markov random field models which incorporate knowledge of these expected shocks in mortality. We demonstrate the potential for these models to improve upon alternatives not incorporating knowledge of expected shocks in a simulation study. We apply these models to estimate U5MR in Rwanda at the national level from 1985 to 2019, a time period which includes the Rwandan civil war and genocide.

Real-time Denoising Algorithm for STEM Imaging Using Markov Random Field Model

Real-time Denoising Algorithm for STEM Imaging Using Markov Random Field Model

New Poisson denoising method for pulse-count STEM imaging

With the recent progress in the development of detectors in electron microscopy, it has become possible to directly count the number of electrons per pixel, even with a scintillator-type detector, by incorporating a pulse-counting module. To optimize a denoising method for electron counting imaging, in this study, we propose a Poisson denoising method for atomic-resolution scanning transmission electron microscopy images. Our method is based on the Markov random field model and Bayesian inference, and we can reduce the electron dose by a factor of about 15 times or further below. Moreover, we showed that the method of reconstruction from multiple images without integrating them performs better than that from an integrated image.

Enhancing Brain Segmentation in MRI through Integration of Hidden Markov Random Field Model and Whale Optimization Algorithm

The automatic delineation and segmentation of the brain tissues from Magnetic Resonance Images (MRIs) is a great challenge in the medical context. The difficulty of this task arises out of the similar visual appearance of neighboring brain structures in MR images. In this study, we present an automatic approach for robust and accurate brain tissue boundary outlining in MR images. This algorithm is proposed for the tissue classification of MR brain images into White Matter (WM), Gray Matter (GM) and Cerebrospinal Fluid (CSF). The proposed segmentation process combines two algorithms, the Hidden Markov Random Field (HMRF) model and the Whale Optimization Algorithm (WOA), to enhance the treatment accuracy. In addition, we use the Whale Optimization Algorithm (WOA) to optimize the performance of the segmentation method. The experimental results from a dataset of brain MR images show the superiority of our proposed method, referred to HMRF-WOA, as compared to other reported approaches. The HMRF-WOA is evaluated on multiple MRI contrasts, including both simulated and real MR brain images. The well-known Dice coefficient (DC) and Jaccard coefficient (JC) were used as similarity metrics. The results show that, in many cases, our proposed method approaches the perfect segmentation with a Dice coefficient and Jaccard coefficient above 0.9.

Disentanglement of Evolutionary Constraints in Statistical Models of Proteins

The exponential growth of protein sequences in the post-genomic era has revolutionized the application of generative sequence models for pivotal tasks such as contact prediction, protein design, alignment, and homology search. Despite remarkable progress in these areas, the interpretability of the modeled pairwise parameters remains limited due to complexities arising from coevolution, phylogeny, and entropy. While post-correction methods for contact prediction have been developed to eliminate entropy-related contributions from predicted contact maps, there is currently no direct approach to correct entropy in other applications reliant on raw parameters. In this paper, we investigate the sources of entropy signal and propose a novel spectral regularizer, LH (an abbreviation of Henri Lebesgue), to mitigate its impact during model fitting. By incorporating this regularizer into the GREMLIN framework (utilizing a Markov random field or Potts model), we enable the accurate inference of sparse contact maps while simultaneously improving interpretability and addressing overfitting concerns critical for sequence evaluation and design. To validate the efficacy of our approach, we design multiple protein sequences based on GREMLIN with both L2 and LH regularizers, and subsequently experimentally measure their using cDNA display proteolysis. Our findings demonstrate that proteins designed using the LH regularizer exhibit increased diversity and enhanced folding stability. Published by the American Physical Society 2024

Fuzzy Parameters Integrated Markov Random Field (MRF) Model for Super Resolution Mapping (SRM) Over Vague Land Cover Regions

Fuzzy Parameters Integrated Markov Random Field (MRF) Model for Super Resolution Mapping (SRM) Over Vague Land Cover Regions

The spatial effects of the household's food insecurity levels in Ethiopia: by ordinal geo-additive model.

Food insecurity and vulnerability in Ethiopia are historical problems due to natural- and human-made disasters, which affect a wide range of areas at a higher magnitude with adverse effects on the overall health of households. In Ethiopia, the problem is wider with higher magnitude. Moreover, this geographical distribution of this challenge remains unexplored regarding the effects of cultures and shocks, despite previous case studies suggesting the effects of shocks and other factors. Hence, this study aims to assess the geographic distribution of corrected-food insecurity levels (FCSL) across zones and explore the comprehensive effects of diverse factors on each level of a household's food insecurity. This study analyzes three-term household-based panel data for years 2012, 2014, and 2016 with a total sample size of 11505 covering the all regional states of the country. An extended additive model, with empirical Bayes estimation by modeling both structured spatial effects using Markov random field or tensor product and unstructured effects using Gaussian, was adopted to assess the spatial distribution of FCSL across zones and to further explore the comprehensive effect of geographic, environmental, and socioeconomic factors on the locally adjusted measure. Despite a chronological decline, a substantial portion of Ethiopian households remains food insecure (25%) and vulnerable (27.08%). The Markov random field (MRF) model is the best fit based on GVC, revealing that 90.04% of the total variation is explained by the spatial effects. Most of the northern and south-western areas and south-east and north-west areas are hot spot zones of food insecurity and vulnerability in the country. Moreover, factors such as education, urbanization, having a job, fertilizer usage in cropping, sanitation, and farming livestock and crops have a significant influence on reducing a household's probability of being at higher food insecurity levels (insecurity and vulnerability), whereas shocks occurrence and small land size ownership have worsened it. Chronically food insecure zones showed a strong cluster in the northern and south-western areas of the country, even though higher levels of household food insecurity in Ethiopia have shown a declining trend over the years. Therefore, in these areas, interventions addressing spatial structure factors, particularly urbanization, education, early marriage control, and job creation, along with controlling conflict and drought effect by food aid and selected coping strategies, and performing integrated farming by conserving land and the environment of zones can help to reduce a household's probability of being at higher food insecurity levels.

Hidden Markov Random Field Model Based VGG-16 for Segmentation and Classification of Head and Neck Cancer

Hidden Markov Random Field Model Based VGG-16 for Segmentation and Classification of Head and Neck Cancer

MCMC algorithm based on Markov random field in image segmentation.

In the realm of digital image applications, image processing technology occupies a pivotal position, with image segmentation serving as a foundational component. As the digital image application domain expands across industries, the conventional segmentation techniques increasingly challenge to cater to modern demands. To address this gap, this paper introduces an MCMC-based image segmentation algorithm based on the Markov Random Field (MRF) model, marking a significant stride in the field. The novelty of this research lies in its method that capitalizes on domain information in pixel space, amplifying the local segmentation precision of image segmentation algorithms. Further innovation is manifested in the development of an adaptive segmentation image denoising algorithm based on MCMC sampling. This algorithm not only elevates image segmentation outcomes, but also proficiently denoises the image. In the experimental results, MRF-MCMC achieves better segmentation performance, with an average segmentation accuracy of 94.26% in Lena images, significantly superior to other common image segmentation algorithms. In addition, the study proposes that the denoising model outperforms other algorithms in peak signal-to-noise ratio and structural similarity in environments with noise standard deviations of 15, 25, and 50. In essence, these experimental findings affirm the efficacy of this study, opening avenues for refining digital image segmentation methodologies.

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.

Identifying the latent relationships between factors associated with traffic crashes through graphical models

Traffic safety field has been oriented toward finding the relationships between crash outcomes and predictor variables to understand crash phenomena and/or predict future crashes. In the literature, the main framework established for this purpose is based on constructing a modelling equation in which crash outcome (e.g., frequencies) is examined in relation to explanatory variables chosen based on the problem at hand. Despite the importance and success of this approach, there are two issues that are generally not discussed: 1) the latent relationships between factors associated with crashes are oftentimes not the focus of analysis or not observed; and 2) there are not many tools to make informed decisions on which variables might have an impact on the crash outcome and should be included in a safety model, particularly when observations are limited. To address these issues, this paper proposes the use of graphical models, namely a Markov random field (MRF) modelling, Bayesian network modelling, and a graphical XGBoost approach, to disclose relationship topologies of explanatory variables leading to fatal and incapacitating injury pedestrian crashes. The application of graph learning models in traffic safety has a high potential because they are not only useful to understand the mechanism behind the crash occurrence but also can assist in devising accurate and reliable prevention measures by identifying the true variable structure and essential factors jointly acting towards crash occurrence, similar to a pathological examination.

Sensitivity analysis of prior distributions in Bayesian graphical modeling: Guiding informed prior choices for conditional independence testing

Bayesian analysis methods provide a significant advancement in network psychometrics, allowing researchers to use the edge inclusion Bayes factor for testing conditional independence between pairs of variables in the network. Using this methodology requires setting prior distributions on the network parameters and on the network’s structure. However, the impact of both prior distributions on the inclusion Bayes factor is underexplored. In this paper, we focus on a specific class of Markov Random Field models for ordinal and binary data. We first discuss the different choices of prior distributions for the network parameters and the network structure, and then perform an extensive simulation study to assess the sensitivity of the inclusion Bayes factor to these distributions. We pay particular attention to the effect of the scale of the prior on the inclusion Bayes factor. To improve the accessibility of the results, we also provide an interactive Shiny app. Finally, we present the R package simBgms, which provides researchers with a user-friendly tool to perform their own simulation studies for Bayesian Markov Random Field models. All of this should help researchers make more informed, evidence-based decisions when preparing to analyze empirical data using network psychometric models.

Satellite imagery retrieval based on adaptive Gaussian–Markov random field model with Bayes deep convolutional neural network

Satellite imagery retrieval based on adaptive Gaussian–Markov random field model with Bayes deep convolutional neural network

Real Aperture Radar Super-Resolution Imaging for Sea Surface Monitoring Based on a Hybrid Model

In recent years, super-resolution imaging techniques have been intensely introduced to enhance the azimuth resolution of real aperture scanning radar (RASR). However, there is a paucity of research on the subject of sea surface imaging with small incident angles for complex scenarios. This research endeavors to explore super-resolution imaging for sea surface monitoring, with a specific emphasis on grounded or shipborne platforms. To tackle the inescapable interference of sea clutter, it was segregated from the imaging objects and was modeled alongside I/Q channel noise within the maximum likelihood framework, thus mitigating clutter’s impact. Simultaneously, for characterizing the non-stationary regions of the monitoring scene, we harnessed the Markov random field (MRF) model for its two-dimensional (2D) spatial representational capacity, augmented by a quadratic term to bolster outlier resilience. Subsequently, the maximum a posteriori (MAP) criterion was employed to unite the ML function with the statistical model regarding imaging scene. This hybrid model forms the core of our super-resolution methodology. Finally, a fast iterative threshold shrinkage method was applied to solve this objective function, yielding stable estimates of the monitored scene. Through the validation of simulation and real data experiments, the superiority of the proposed approach in recovering the monitoring scenes and clutter suppression has been verified.

Single image dehazing via decomposition and enhancement

AbstractHazy images suffer from two problems. The low contrast can be enhanced by estimating a transmission layer, and the colour cast can be restored by estimating an airlight. These two variables, together with the albedo layer, are the constitutive elements of a hazy image. The resulting quality of dehazed images is inextricably linked to the accurate estimation of these components. However, it is ill‐posed to decompose these variables from a single image. As such, this paper presents an innovative algorithm intended to facilitate the optimal decomposition of a hazy image. Using the Markov random field model, an optimal framework is established that allows the simultaneous estimation of the three components across the three‐colour channels. To improve the visual quality, three improvements are proposed in the variational solution for the optimal components. The dehazed result is recomposed from the components with the transmission enhanced to circumvent any potential artefacts or information loss. Extensive experiments on natural images corroborate that the proposed algorithm outperforms state‐of‐the‐art dehazing methods, both qualitatively and quantitatively.

Polarimetric Synthetic Aperture Radar Image Classification Based on Double-Channel Convolution Network and Edge-Preserving Markov Random Field

Deep learning methods have gained significant popularity in the field of polarimetric synthetic aperture radar (PolSAR) image classification. These methods aim to extract high-level semantic features from the original PolSAR data to learn the polarimetric information. However, using only original data, these methods cannot learn multiple scattering features and complex structures for extremely heterogeneous terrain objects. In addition, deep learning methods always cause edge confusion due to the high-level features. To overcome these limitations, we propose a novel approach that combines a new double-channel convolutional neural network (CNN) with an edge-preserving Markov random field (MRF) model for PolSAR image classification, abbreviated to “DCCNN-MRF”. Firstly, a double-channel convolution network (DCCNN) is developed to combine complex matrix data and multiple scattering features. The DCCNN consists of two subnetworks: a Wishart-based complex matrix network and a multi-feature network. The Wishart-based complex matrix network focuses on learning the statistical characteristics and channel correlation, and the multi-feature network is designed to learn high-level semantic features well. Then, a unified network framework is designed to fuse two kinds of weighted features in order to enhance advantageous features and reduce redundant ones. Finally, an edge-preserving MRF model is integrated with the DCCNN network. In the MRF model, a sketch map-based edge energy function is designed by defining an adaptive weighted neighborhood for edge pixels. Experiments were conducted on four real PolSAR datasets with different sensors and bands. The experimental results demonstrate the effectiveness of the proposed DCCNN-MRF method.

Hidden Markov random field models for cell-type assignment of spatially resolved transcriptomics.

The recent development of spatially resolved transcriptomics (SRT)technologies has facilitated research on gene expression in the spatial context. Annotating cell types is one crucial step for downstream analysis. However, many existing algorithms use an unsupervised strategy to assign cell types for SRT data. They first conduct clustering analysis and then aggregate cluster-level expression based on the clustering results. This workflow fails to leverage the marker gene information efficiently. On the other hand, other cell annotation methods designed for single-cell RNA-seq data utilize the cell-type marker genes information but fail to use spatial information in SRT data. We introduce a statistical spatial transcriptomics cell assignment model, SPAN, to annotate clusters of cells or spots into known types in SRT data with prior knowledge of predefined marker genes and spatial information. The SPAN model annotates cells or spots from SRT data using predefined overexpressed marker genes and combines a mixture model with a hidden Markov random field to model the spatial dependency between neighboring spots. We demonstrate the effectiveness of SPAN against spatial and nonspatial clustering algorithms through extensive simulation and real data experiments. https://github.com/ChengZ352/SPAN.