Markov Random Field Theory Research Articles

Bayesian inference for long memory term structure models

In this study, we propose a novel adaptation of the Dynamic Nelson–Siegel term structure model, incorporating long memory properties to enhance its forecasting accuracy. Our approach involves modelling the evolution of latent factors using fractional Gaussian noise processes, approximated by a weighted sum of independent first-order autoregressive components. The resulting formulation allows for a Gaussian Markov Random Field representation, facilitating the application of computationally efficient Bayesian techniques through Integrated Nested Laplace Approximations. Extensive simulation and empirical analysis demonstrate that integrating long memory significantly improves the model's forecasting performance, particularly for longer time horizons. By shedding light on the potential benefits of incorporating long memory concepts into traditional term structure models, our research highlights its utility in capturing intricate temporal dependencies and enhancing prediction precision.

An automated method for tendon image segmentation on ultrasound using grey-level co-occurrence matrix features and hidden Gaussian Markov random fields

Background:Despite knowledge of qualitative changes that occur on ultrasound in tendinopathy, there is currently no objective and reliable means to quantify the severity or prognosis of tendinopathy on ultrasound. Objective:The primary objective of this study is to produce a quantitative and automated means of inferring potential structural changes in tendinopathy by developing and implementing an algorithm which performs a texture based segmentation of tendon ultrasound (US) images. Method:A model-based segmentation approach is used which combines Gaussian mixture models, Markov random field theory and grey-level co-occurrence (GLCM) features. The algorithm is trained and tested on 49 longitudinal B-mode ultrasound images of the Achilles tendons which are labelled as tendinopathic (24) or healthy (25). Hyperparameters are tuned, using a training set of 25 images, to optimise a decision tree based classification of the images from texture class proportions. We segment and classify the remaining test images using the decision tree. Results:Our approach successfully detects a difference in the texture profiles of tendinopathic and healthy tendons, with 22/24 of the test images accurately classified based on a simple texture proportion cut-off threshold. Results for the tendinopathic images are also collated to gain insight into the topology of structural changes that occur with tendinopathy. It is evident that distinct textures, which are predominantly present in tendinopathic tendons, appear most commonly near the transverse boundary of the tendon, though there was a large variability among diseased tendons. Conclusion:The GLCM based segmentation of tendons under ultrasound resulted in distinct segmentations between healthy and tendinopathic tendons and provides a potential tool to objectively quantify damage in tendinopathy.

Improving Differential Interferometry Synthetic Aperture Radar Phase Unwrapping Accuracy with Global Navigation Satellite System Monitoring Data

: We developed a GNSS-assisted InSAR phase unwrapping algorithm for large-deformation DInSAR data processing in coal mining areas. Utilizing the Markov random field (MRF) theory and simulated annealing, the algorithm derived the energy function using MRF theory, Gibbs distribution, and the Hammersley–Clifford theorem. It calculated an image probability ratio and unwrapped the phase through iterative calculations of the initial integer perimeter matrix, interference phase, and weight matrix. Algorithm reliability was confirmed by combining simulated phases with digital elevation model (DEM) data for deconvolution calculations, showing good agreement with real phase-value results (median error: 4.8 × 10−4). Applied to ALOS-2 data in the Jinfeng mining area, the algorithm transformed interferometric phase into deformation, obtaining simulated deformation by fitting GNSS monitoring data. It effectively solved meter-scale deformation variables between single-period images, particularly for unwrapping problems due to decoherence. To improve calculation speed, a coherence-based threshold was set. Points with high coherence avoided iterative optimization, while points below the threshold underwent iterative optimization (coherence threshold: 0.32). The algorithm achieved a median error of 30.29 mm and a relative error of 2.5% compared to GNSS fitting results, meeting accuracy requirements for mining subsidence monitoring in large mining areas.

A Dynamic Partition Model for Multi-Energy Power Grid Energy Balance Considering Electric Vehicle Response Willingness

In multi-energy power grids in which electric vehicles (EVs) participate in response, there are significant differences in the power balance between multi-energy supply and load at different time scales and spatial scales. To optimize the energy balance demand of each region, this paper proposes a dynamic partition coordination model for power grid energy regulation demand that considers the willingness of electric vehicles to respond and the uncertainties related to sources, loads, and storage. Firstly, the charging and discharging characteristics of multi-energy conversion devices in power grids, as well as the response uncertainties of these devices, are studied, and a source, load, and storage uncertainty model is established. Then, based on the Markov random field theory and the energy prior model, the dynamic partition model and its solution algorithm for the multi-energy power grid are proposed. Finally, a simulation system is established based on the actual operating data of a multi-energy power grid, and the proposed method is simulated and analyzed. The results indicate that the energy balance partition optimization method proposed in this article is effective. The application of the method proposed in this article can fully leverage the regulatory potential of energy conversion equipment, effectively reduce the proportion of traditional energy supply and peak shaving capacity, and improve the utilization rate of renewable energy.

A New Approach for 4-D Exospheric Tomography Based on Optimal Interpolation and Gaussian Markov Random Fields

Exospheric tomography is a computational 3-D imaging technique that provides the estimates of the neutral density distributions of the terrestrial exosphere from space-based ultraviolet (UV) measurements. Variability of neutral densities during geomagnetically active conditions has been previously reported, motivating the development of time-dependent tomographic techniques that can characterize both the spatial and temporal scales of densities during these events. However, solving the dynamic exospheric tomography problem can be challenging owing to its ill-posedness. In this letter, we introduce a novel algorithm for 4-D exospheric tomography based on optimal interpolation (OI) and Gaussian Markov random field (GMRF) theory. The OI analysis enables iterative reconstructions of the exosphere when a statistical background field is provided. Its mean is selected from previous knowledge of the exosphere, and its covariance matrix is estimated using GMRF. To validate the performance, we apply our proposed methodology to six days of UV data acquired by National Aeronautics and Space Administration (NASA) two-wide angle imaging neutral-atom spectrometer (TWINS) mission during the geomagnetic storm that occurred on June 15, 2008.

Lane Line Identification and Research Based on Markov Random Field

In view of the poor robustness and low accuracy in lane line identification based on digital image processing, this paper proposes a Markov random field intelligent algorithm based on machine learning to identify lane lines. The complete lane line identification steps are as follows: First, high-quality traffic scenario images are created by means of image preprocessing, which includes image graying, grayscale transformation, and the extraction of regions of interest (ROIs). Then, the images are modeled according to Markov random field theory, and model reasoning is performed based on the binary graph cut method. In the reasoning process, to achieve accurate lane line segmentation, i.e., the optimal solution of the model, the energy potential function is introduced to optimize the binary graph cut method. Finally, the lane line pixel label is marked according to the segmentation result. The experiments showed that the algorithm could accurately segment the lane line pixels after only 10 iterations, indicating that the identification method has good performance in both reasoning speed and identification accuracy, which takes account of both accuracy and real-time processing, and can meet the requirements of lane recognition for lightweight automatic driving systems.

Influence of geological uncertainty on the design of OWTF monopiles

This paper presents a methodology to assess the influence of geological uncertainty (stratigraphic uncertainty) on designing an offshore wind turbine foundation (OWTF). To consider the stratigraphic uncertainty, we create a synthetic stratigraphic model (SSM) and then sample multiple sets of boreholes to develop a series of stratigraphic models, each with a different degree of uncertainty (entropy). Using Markov random field (MRF) theory, these stratigraphic models were simulated, and their entropies were evaluated. The results indicate the entropies of the stratigraphic models decrease as the number of boreholes increases. The OWTF monopile is then designed based on these stratigraphic models with different entropy levels. Next, Monte Carlo simulation (MCS) is used to evaluate the failure probability of the design, considering uncertainties of the stratigraphic model and soil properties. Then, two monopile designs simulating piles located at different stratigraphic configurations are analyzed to assess the effects of stratigraphic uncertainty and strength parameter variability on their failure probabilities. Finally, insights gained regarding the effect of stratigraphic uncertainty on the OWTF monopile design are discussed.

Fuzzy Active Contour Model With Markov Random Field for Change Detection

The traditional active contour models are sensitive to the speckle noise in the synthetic aperture radar (SAR) images. In this paper, the Markov random field (MRF) theory is incorporated into the fuzzy active contour model to detect the changes of multitemporal SAR images. In the proposed method, neighboring information is considered to modify the pointwise prior probability for exploiting the mutual and spatial information. In addition, we incorporate MRF into the fuzzy active contour model and get the resulting MRF-based energy function. Finally, we drive the associated first variation of the energy function to compute the fuzzy membership. Due to the introduction of MRF, the proposed MRF-based fuzzy active contour model is robust to the speckle noise in the SAR images and can achieve accurate change detection results. Experiments on four SAR image datasets demonstrate that the proposed MRF-based fuzzy active contour model is able to accurately segment the difference image and has better performance in comparison with other change detection techniques.

A Study on Application of Markov Random Fields in Image Restoration and its Efficiency

Image restoration has been a popular and active field of research for decades. Images are destroyed when exposed to ‘noise’ which can occur due to physical contact or electrical/electronic interference. Here, Bayesian statistical techniques and Markov random field (MRF) theory were used to restore a black and white binary image corrupted by additive Gaussian noise with zero mean and constant variance. The binary image was used as a Markov random field. An image is comprised of pixels and these pixels have a regular two-dimensional lattice structure. A matrix including ±1 values was generated randomly. It was represented and interpreted as an Ising model in Statistical Mechanics. The probability distribution of the Ising model was used as the prior distribution (a Gibbs or Boltzmann distribution). Likelihood function was obtained by using the random matrix and the observed corrupted image. Markov Chain Monte Carlo (MCMC) method was used to simulate posterior distribution which again turns out to be a Gibbs or Boltzmann distribution. More specifically, Metropolis-Hastings algorithm which is one of the popular MCMC algorithms was used in this simulation. In this study, Peak Signal to Noise Ratio (PSNR) and Mean Squared Error (MSE) methods were used to measure the quality of restored images. MATLAB (R2013a (8.1.0.604)) was used to construct the program in this research work. Finally, high quality images were restored which were almost similar to the original image. A decrease in restored image quality was observed with the increase in noise. When the image size was increased, a higher number of iterations was required to obtain an acceptable level of quality in the restored image.

Texture synthesis: A novel method for generating digital models with heterogeneous diversity of rock materials and its CGM verification

The interaction of meso-structures determines the macro-mechanical properties of rock material. Therefore, reliable description of heterogeneous diversity in rock is of great significance for studying its mechanical response and fracturing process. Based on the Markov random field theory, the texture synthesis method is optimized in terms of input exemplar and its best matching neighborhood size by using the mean shift clustering algorithm and the color histogram statistics. The optimized method can generate many parallel images of rock materials which have the function of feature replication and the characteristics of diverse heterogeneity. The reliability of the heterogeneous diversity models generated by the texture synthesis method is verified from three fundamental levels, including the CIELab color space, the geometric parameters of particles, and the numerical mechanical properties (CGM). The stress–strain curves and damage evolution processes of synthetic digital models under uniaxial compression have a strong characterization ability. Therefore, this new digital modeling method that represents the structural details and heterogeneous diversity of rock material can be utilized for evaluating the composition similarity and heterogeneous geometric features, and provide abundant materials for subsequent numerical mechanical analysis. This method provides a new idea for studying the meso-mechanical properties and failure mechanism of rock materials.

Tumor heterogeneity estimation for radiomics in cancer.

Radiomics is an emerging field of medical image analysis research where quantitative measurements are obtained from radiological images that can be utilized to predict patient outcomes and inform treatment decisions. Cancer patients routinely undergo radiological evaluations when images of various modalities including computed tomography, positron emission tomography, and magnetic resonance images are collected for diagnosis and for evaluation of disease progression. Tumor characteristics, often referred to as measures of tumor heterogeneity, can be computed using these clinical images and used as predictors of disease progression and patient survival. Several approaches for quantifying tumor heterogeneity have been proposed, including intensity histogram-based measures, shape and volume-based features, and texture analysis. Taking into account the topology of the tumors we propose a statistical framework for estimating tumor heterogeneity using clustering based on Markov random field theory. We model the voxel intensities using a Gaussian mixture model using a Gibbs prior to incorporate voxel neighborhood information. We propose a novel approach to choosing the number of mixture components. Subsequently, we show that the proposed procedure outperforms the existing approaches when predicting lung cancer survival.

Skin Lesion Segmentation Using Stochastic Region-Merging and Pixel-Based Markov Random Field

Markov random field (MRF) theory has achieved great success in image segmentation. Researchers have developed various methods based on MRF theory to solve skin lesions segmentation problems such as pixel-based MRF model, stochastic region-merging approach, symmetric MRF model, etc. In this paper, the proposed method seeks to provide a complement to the advantages of the pixel-based MRF model and stochastic region-merging approach. This is in order to overcome shortcomings of the pixel-based MRF model, because of various challenges that affect the skin lesion segmentation results such as irregular and fuzzy border, noisy and artifacts presence, and low contrast between lesions. The strength of the proposed method lies in the aspect of combining the benefits of the pixel-based MRF model and the stochastic region-merging by decomposing the likelihood function into the multiplication of stochastic region-merging likelihood function and the pixel likelihood function. The proposed method was evaluated on bench marked available datasets, PH2 and ISIC. The proposed method achieves Dice coefficients of 89.65 % on PH2 and 88.34 % on ISIC datasets respectively.

RETRACTED: Real time speech recognition algorithm on embedded system based on continuous Markov model

Abstract Real time speech recognition technology, as a key cross technology in the field of artificial intelligence in recent years, has been widely used in the fields of intelligent voice toys, industrial control and intelligent rehabilitation. Because the real-time speech recognition technology based on embedded technology has obvious advantages in the volume, power consumption and research and development cost of the system, it has become a hot carrier to achieve efficient speech recognition technology. In order to realize a simple and practical real-time speech recognition system based on embedded system, this paper designs a basic framework of machine learning based on Markov random field theory combined with machine learning theory, and studies the algorithm of real-time speech vocabulary matching recognition based on this framework. In detail, the algorithm proposed in this paper will process the speech signal from the aspects of preprocessing, signal detection, feature extraction and quantization. Finally, this paper will build a real-time speech recognition system based on DSP processor. The experimental results show that the real-time speech recognition algorithm proposed in this paper can improve the real-time recognition speed of the system. The corresponding speed changes from about 12 s to about 200 ms, and the corresponding real-time accuracy rate increases to about 95%.

Symmetry Information Based Fuzzy Clustering for Infrared Pedestrian Segmentation

Pedestrian detection in infrared images is always a challenging task. Segmentation is an important step of pedestrian detection. An accurate segmentation could provide more information for further analysis. In this paper, an improved Fuzzy C-Means clustering method, which incorporates geometric symmetry information, is proposed for infrared pedestrian segmentation. In the proposed method, symmetry information is introduced by Markov random field theory. Moreover, a new metric is utilized to handle the weak symmetry of pedestrian. In addition, a whole procedure is proposed to extract infrared pedestrians. The experimental results indicate that our method performs better for infrared pedestrian segmentation and obtains better segmentation results compared with other state-of-the-art methods.

Low-Power Noise-Immune Nanoscale Circuit Design Using Coding-Based Partial MRF Method

Reliability is one of the major concerns for ultralow power circuit designs. Markov random field (MRF) techniques have been applied to logic circuits to resist random noise when operating under ultralow supply voltage or sub-threshold voltage. Although conventional MRF networks can be easily mapped onto simple logic circuits, it becomes difficult when the circuits are large and complex. In this paper, we present a general coding-based partial MRF (CPMRF) method for multi-logic operations in one basic unit, which is referred to as a CPMRF pair. A CPMRF pair saves circuit area by sharing a common MRF network. It also inherits noise immunity from the MRF theory while obtaining noise immunity from the coding structure as a combination of robust “1s” and “0s.” The resulting architectures become more cost effective than conventional ones. To validate the performance of our proof-of-concept design, we fabricated a carry-lookahead adder implemented by the proposed CPMRF pairs using IBM 130-nm CMOS technology. Measurement results indicate that the CPMRF CLA can achieve high noise tolerance with 20% improvement while occupying 37.7% less area and reducing power consumption by 93% compared with the master-and-slave MRF CLA design.

Feedback-Based Low-Power Soft-Error-Tolerant Design for Dual-Modular Redundancy

Triple-modular redundancy (TMR), which consists of three identical modules and a voting circuit, is a common architecture for soft-error tolerance. However, the original TMR suffers from two major drawbacks: the large area overhead and the vulnerability of the voter. In order to overcome these drawbacks, we propose a new complementary dual-modular redundancy (CDMR) scheme for mitigating the effect of soft errors. Inspired by the Markov random field (MRF) theory, a two-stage voting system is implemented in CDMR, including a first-stage optimal MRF structure and a second-stage high-performance merging unit. The CDMR scheme can reduce the voting circuit area by 20% while saving the area of one redundant module, achieving at least 26% error-rate reduction at an ultralow supply voltage of 0.25 V with 8.33% faster timing compared to previous voter designs.

Efficient Compression of Encrypted Binary Images Using the Markov Random Field

Similar to conventional compression with the original, unencrypted image as the input, the recently emerged compression on encrypted images generally exploits statistical correlation of natural images to improve compression efficiency. Most of these compression schemes in the literature leverage statistical correlation at the content-owner or service-provider side, which would either increase the computational burden on the content-owner or disclose statistical distributions to the service-provider and thus probably hinder their practical applications. Through analysis on properties of the compression system for encrypted data, we believe that it is more preferable to exploit statistical correlation of natural images at the receiver side with both encryption key and sufficient computational capability, which in turn would improve compression efficiency while achieving low computational complexity and sufficient security for the content owner and the service provider. In light of this, we use the Markov random field (MRF) to characterize binary images in the spatial domain and represent it with a factor graph. The constructed MRF representation of the binary image in the factor graph is then integrated seamlessly with the factor graph for low-density parity check (LDPC)-based decompression, yielding a joint factor graph for binary image reconstruction. By deriving message update equations for the joint factor graph, we develop a new lossless compression scheme for encrypted binary images, which involves stream-cipher-based encryption, LDPC-based compression, and factor-graph-based image reconstruction. Preferable parameters for the proposed scheme are first determined numerically on a specific binary image and then applied to other binary images. Extensive simulations show that significant improvements in terms of compression bit rate over the state of the art are achieved, demonstrating the feasibility and effectiveness of the proposed scheme.

Exploring risk factors in breast cancer screening program data using structured geoadditive models with high order interaction

When analyzing data from cancer screening programs, flexible regression specifications are required to account for the highly complex structure in such data. We analyzed data from a breast cancer screening program conducted in central Portugal and considered an extension of structured additive regression models where, in addition to the possibility to include nonlinear and spatial effects, we can include a trivariate interaction between attendance rate, detection rate and mortality rate in the screening program. While spatial effects capture unobserved heterogeneity at the municipality level, the trivariate interaction proves important for the understanding of the complex interaction effects resulting from the diversity in municipality coverage and attendance rates. The trivariate interaction is implemented based on a Markov random field representation which enables efficient Bayesian inference and, when modeling breast cancer incidence rates, showed a significant improvement in terms of model fit when compared to a simpler geoadditive regression model.

Theoretical generalization of Markov chain random field from potential function perspective

The inner relationship between Markov random field (MRF) and Markov chain random field (MCRF) is discussed. MCRF is a special MRF for dealing with high-order interactions of sparse data. It consists of a single spatial Markov chain (SMC) that can move in the whole space. Generally, the theoretical backbone of MCRF is conditional independence assumption, which is a way around the problem of knowing joint probabilities of multi-points. This so-called Naive Bayes assumption should not be taken lightly and should be checked whenever possible because it is mathematically difficult to prove. Rather than trap in this independence proving, an appropriate potential function in MRF theory is chosen instead. The MCRF formulas are well deduced and the joint probability of MRF is presented by localization approach, so that the complicated parameter estimation algorithm and iteration process can be avoided. The MCRF model is then applied to the lithofacies identification of a region and compared with triplex Markov chain (TMC) simulation. Analyses show that the MCRF model will not cause underestimation problem and can better reflect the geological sedimentation process.

Quantifying stratigraphic uncertainties by stochastic simulation techniques based on Markov random field

Stratigraphic (or lithological) uncertainty refers to the uncertainty of boundaries between different soil layers and lithological units, which has received increasing attention in geotechnical engineering. In this paper, an effective stochastic geological modeling framework is proposed based on Markov random field theory, which is conditional on site investigation data, such as observations of soil types from ground surface, borehole logs, and strata orientation from geophysical tests. The proposed modeling method is capable of accounting for the inherent heterogeneous and anisotropic characteristics of geological structure. In this method, two modeling approaches are introduced to simulate subsurface geological structures to accommodate different confidence levels on geological structure type (i.e., layered vs. others). The sensitivity analysis for two modeling approaches is conducted to reveal the influence of mesh density and the model parameter on the simulation results. Illustrative examples using borehole data are presented to elucidate the ability to quantify the geological structure uncertainty. Furthermore, the applicability of two modeling approaches and the behavior of the proposed model under different model parameters are discussed in detail. Finally, Bayesian inferential framework is introduced to allow for the estimation of the posterior distribution of model parameter, when additional or subsequent borehole information becomes available. Practical guidance of using the proposed stochastic geological modeling technique for engineering practice is given.