Gaussian Markov Random Field Research Articles

Efficient experimental sampling through low-rank matrix recovery

Low-rank matrix recovery allows a low-rank matrix to be reconstructed when only a fraction of its elements is available. In this paper, an approximate Bayesian approach to low-rank matrix recovery is developed and its potential benefit for an application in metrology explored. The approach extends a recently proposed Bayesian low-rank matrix recovery procedure by utilizing a Gaussian Markov random field (GMRF) prior. The GMRF prior accounts for spatial smoothness, which is relevant for applications such as quantitative magnetic resonance imaging and nano Fourier transform infrared (FTIR) spectroscopy. The approach proposed here is automatic in that its hyperparameters are estimated from the data. Application to nano-FTIR spectroscopy demonstrates that the effort required to perform experiments in the time-consuming measurement of multi-dimensional data can be reduced significantly. Software for the proposed approach is available upon request.

Application of High‐Resolution Remote Sensing Image for Individual Tree Identification of Pinus sylvestris and Pinus tabulaeformis

Aiming at applying unmanned aerial vehicle (UAV) remote sensing technology in extracting individual standing tree information, a new automatic single‐tree information extraction method is proposed in this paper. The spectral information enhancement processing was performed on the original UAV image to highlight detailed local features; by importing DBI index, the optimal cluster number of the K‐means clustering was automatically determined, and image pixels were then marked; Gauss Markov random field (GMRF) model was employed to segment the image further; by mathematical morphology, operators to postprocess the segmentation results to obtain the individual standing tree crown information, and individual standing tree position was calculated through image geometric moment as the basis for its identification. The results show that with the proposed extraction method, the overall accuracy of standing tree identification for the Pinus sylvestris and Pinus tabulaeformis forest areas are 95.65% and 89.52%; the single‐tree crown extraction accuracy is 95.65% and 81.90%, respectively. This method exhibits good applicability while it does not require a large amount of manual intervention and prior knowledge, which significantly improves the automation of information extraction.

Non-local spatially varying finite mixture models for image segmentation

In this work, we propose a new Bayesian model for unsupervised image segmentation based on a combination of the spatially varying finite mixture models (SVFMMs) and the non-local means (NLM) framework. The probabilistic NLM weighting function is successfully integrated into a varying Gauss–Markov random field, yielding a prior density that adaptively imposes a local regularization to simultaneously preserve edges and enforce smooth constraints in homogeneous regions of the image. Two versions of our model are proposed: a pixel-based model and a patch-based model, depending on the design of the probabilistic NLM weighting function. Contrary to previous methods proposed in the literature, our approximation does not introduce new parameters to be estimated into the model, because the NLM weighting function is completely known once the neighborhood of a pixel is fixed. The proposed model can be estimated in closed-form solution via a maximum a posteriori (MAP) estimation in an expectation–maximization scheme. We have compared our model with previously proposed SVFMMs using two public datasets: the Berkeley Segmentation dataset and the BRATS 2013 dataset. The proposed model performs favorably to previous approaches in the literature, achieving better results in terms of Rand Index and Dice metrics in our experiments.

Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix

<p style='text-indent:20px;'>We present an ensemble filtering method based on a linear model for the precision matrix (the inverse of the covariance) with the parameters determined by Score Matching Estimation. The method provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. The parameters are found by solving a system of linear equations. The analysis step uses the inverse formulation of the Kalman update. Several filter versions, differing in the construction of the analysis ensemble, are proposed, as well as a Score matching version of the Extended Kalman Filter.</p>

Statistical Graph Signal Recovery Using Variational Bayes

This brief investigates the problem of Graph Signal Recovery (GSR) when the topology of the graph is not known in advance. In this brief, the elements of the weighted adjacency matrix is statistically related to normal distribution and the graph signal is assumed to be Gaussian Markov Random Field (GMRF). Then, the problem of GSR is solved by a Variational Bayes (VB) algorithm in a Bayesian manner by computing the posteriors in a closed form. The posteriors of the elements of weighted adjacency matrix are proved to have a new distribution which we call it Generalized Compound Confluent Hypergeometric (GCCH) distribution. Moreover, the variance of the noise is estimated by calculating its posterior via VB. The simulation results on synthetic and real-world data shows the superiority of the proposed Bayesian algorithm over some state-of-the-art algorithms in recovering the graph signal.

OTHR multitarget tracking with a GMRF model of ionospheric parameters

The ionosphere is the propagation medium for radio waves transmitted by an over-the-horizon radar (OTHR). Ionospheric parameters, typically, virtual ionospheric heights (VIHs), are required to perform coordinate registration for OTHR multitarget tracking and localization. The inaccuracy of ionospheric parameters has a significant deleterious effect on the target localization of OTHR. Therefore, to improve the localization accuracy of OTHR, it is important to develop accurate models and estimation methods of ionospheric parameters and the corresponding target tracking algorithms. In this paper, we consider the variation of the ionosphere with location and the spatial correlation of the ionosphere. We use a Gaussian Markov random field (GMRF) to model the VIHs, providing a more accurate representation of the VIHs for OTHR target tracking. Based on expectation-conditional maximization and GMRF modeling of the VIHs, we propose a novel joint optimization solution, namely ECM-GMRF, to perform target state estimation, multipath data association and VIHs estimation simultaneously. In ECM-GMRF, the measurements from both ionosondes and OTHR are exploited to estimate the VIHs, leading to a better estimation of the VIHs which improves the accuracy of data association and target state estimation, and vice versa. The simulation indicates the effectiveness of the proposed algorithm.

Error Analysis for Status Update From Sensors With Temporally and Spatially Correlated Observations

This paper studies the status update performance in wireless sensor networks when status, describing the physical reality that is being sensed, is temporally and spatially correlated. The status is modeled as a time-varying Gauss-Markov Random Field (GMRF), whereby the estimation error of status update at the fusion center is analyzed. The transmission latency introduced by wireless networks is modeled as exponentially distributed random variables. We extend the existing queuing analysis results for Age of Information (AoI) with uncorrelated sources to GMRF in the considered scenario. Closed-form expressions of average remote estimation error are obtained for both one- and two-dimensional GMRFs assuming the exponential time-correlation function, both First-Come First-Served (FCFS) and Last-Come First-Served (LCFS) service disciplines, and a single wireless link. The analytical results are then extended to scenarios wherein multi-packet reception, i.e., multiple concurrent wireless links, is enabled; the difficulty of analyzing obsolete updates in this case is addressed leveraging a reasonable approximation validated by theoretical analysis in the regime where the number of sensors is far more than that of wireless links. Monte-Carlo simulation results are also presented which agree with our theoretical analysis. Based on the results, optimal time and spatial domain sampling rates (e.g., sensor density) can be obtained, providing helpful guidance to wireless sensor deployment.

Exposure to and experience of self-harm and self-harm related content: An exploratory network analysis

Exposure to the self-harm behaviour of others plays a role in individuals’ own self-harm thoughts and behaviours, but there has been little consideration of the broader range of mediums through which exposure to self-harm related content may occur. N = 477 participants completed an online study, including questions regarding lifetime history of self-harm thoughts and behaviours and the frequency with which they had been exposed to self-harm via various mediums. Gaussian Markov random field network models were estimated using graphical LASSO and extended Bayesian information criterion. Bootstrapping revealed that exposure mediums with a direct connection to self-harm thoughts and behaviours were the internet (rrp = .34, 95% CI [.26, .42]) and in-passing ‘miscellaneous’ exposure (rrp = .14, 95% CI [.00, .23]). However, stability of the network centrality was low (expected influence stability = 0.52). The node with the greatest increase in expected influence within the network was miscellaneous “in-passing” exposure. In-passing exposure is an understudied exposure medium. Our results may suggest new types of exposure mediums for future research. Data were cross-sectional, so temporal relationships between exposure and behaviour could not be determined. Low stability of the networks suggests that future similar studies would benefit from larger sample sizes.

Locally adaptive Bayesian birth-death model successfully detects slow and rapid rate shifts.

Birth-death processes have given biologists a model-based framework to answer questions about changes in the birth and death rates of lineages in a phylogenetic tree. Therefore birth-death models are central to macroevolutionary as well as phylodynamic analyses. Early approaches to studying temporal variation in birth and death rates using birth-death models faced difficulties due to the restrictive choices of birth and death rate curves through time. Sufficiently flexible time-varying birth-death models are still lacking. We use a piecewise-constant birth-death model, combined with both Gaussian Markov random field (GMRF) and horseshoe Markov random field (HSMRF) prior distributions, to approximate arbitrary changes in birth rate through time. We implement these models in the widely used statistical phylogenetic software platform RevBayes, allowing us to jointly estimate birth-death process parameters, phylogeny, and nuisance parameters in a Bayesian framework. We test both GMRF-based and HSMRF-based models on a variety of simulated diversification scenarios, and then apply them to both a macroevolutionary and an epidemiological dataset. We find that both models are capable of inferring variable birth rates and correctly rejecting variable models in favor of effectively constant models. In general the HSMRF-based model has higher precision than its GMRF counterpart, with little to no loss of accuracy. Applied to a macroevolutionary dataset of the Australian gecko family Pygopodidae (where birth rates are interpretable as speciation rates), the GMRF-based model detects a slow decrease whereas the HSMRF-based model detects a rapid speciation-rate decrease in the last 12 million years. Applied to an infectious disease phylodynamic dataset of sequences from HIV subtype A in Russia and Ukraine (where birth rates are interpretable as the rate of accumulation of new infections), our models detect a strongly elevated rate of infection in the 1990s.

Urban 3D imaging using airborne TomoSAR: Contextual information-based approach in the statistical way

Synthetic aperture radar (SAR) tomography (TomoSAR) technique can eliminate severe overlap in 2D images, and improve target recognition and 3D modeling capabilities, which has become an important trend in SAR development. In recent years, rapid progress has been made and various algorithms were proposed. The Aerospace Information Research Institute, Chinese Academy of Sciences produced the first airborne array TomoSAR system in China. In this paper an airborne TomoSAR experiment using this system and the overall processing flow considering the characteristics of this system are introduced. So far, most of the 3D imaging algorithms used in TomoSAR processing are conducted pixel by pixel, which ignore the structural connections among adjacent pixels. The results will be corrupted by outliers and artifacts due to noise or other uncertainties during processing. To solve this problem, the contextual information of SAR images are explored and utilized by means of the Local Gaussian Markov Random Field (LGMRF) in our 3D reconstruction method. Comparisons with traditional methods are presented to verify the effectiveness of proposed method. The overall processing methods are applied to the data acquired in this experiment and a large scale urban 3D point cloud is obtained, which verifies the ability of the entire system in 3D imaging. This paper presents both the algorithms and experimental results of airborne TomoSAR system, which will contribute in several ways to our understanding of SAR 3D imaging and provide a basis for further research.

Rapid Discrete Optimization via Simulation with Gaussian Markov Random Fields

Inference-based optimization via simulation, which substitutes Gaussian process (GP) learning for the structural properties exploited in mathematical programming, is a powerful paradigm that has been shown to be remarkably effective in problems of modest feasible-region size and decision-variable dimension. The limitation to “modest” problems is a result of the computational overhead and numerical challenges encountered in computing the GP conditional (posterior) distribution on each iteration. In this paper, we substantially expand the size of discrete-decision-variable optimization-via-simulation problems that can be attacked in this way by exploiting a particular GP—discrete Gaussian Markov random fields—and carefully tailored computational methods. The result is the rapid Gaussian Markov Improvement Algorithm (rGMIA), an algorithm that delivers both a global convergence guarantee and finite-sample optimality-gap inference for significantly larger problems. Between infrequent evaluations of the global conditional distribution, rGMIA applies the full power of GP learning to rapidly search smaller sets of promising feasible solutions that need not be spatially close. We carefully document the computational savings via complexity analysis and an extensive empirical study. Summary of Contribution: The broad topic of the paper is optimization via simulation, which means optimizing some performance measure of a system that may only be estimated by executing a stochastic, discrete-event simulation. Stochastic simulation is a core topic and method of operations research. The focus of this paper is on significantly speeding-up the computations underlying an existing method that is based on Gaussian process learning, where the underlying Gaussian process is a discrete Gaussian Markov Random Field. This speed-up is accomplished by employing smart computational linear algebra, state-of-the-art algorithms, and a careful divide-and-conquer evaluation strategy. Problems of significantly greater size than any other existing algorithm with similar guarantees can solve are solved as illustrations.

A Facial Expression Recognition Model Based on Texture and Shape Features

With the development of computer vision, facial expression recognition has become a research hotspot. To further improve the accuracy of facial expression recognition, this paper probes deep into image segmentation, feature extraction, and facial expression classification. Firstly, the convolution neural network (CNN) was adopted to accurately separate the salient regions from the face image. Next, the Gaussian Markov random field (GMRF) model was improved to enhance the ability of texture features to represent image information, and a novel feature extraction algorithm called specific angle abundance entropy (SAAE) was designed to improve the representation ability of shape features. After that, the texture features were combined with shape features, and trained and classified by the support vector machine (SVM) classifier. Finally, the proposed method was compared with common methods of facial expression recognition on a standard facial expression database. The results show that our method can greatly improve the accuracy of facial expression recognition.

Reduced-Dimensional Monte Carlo Maximum Likelihood for Latent Gaussian Random Field Models

Monte Carlo maximum likelihood (MCML) provides an elegant approach to find maximum likelihood estimators (MLEs) for latent variable models. However, MCML algorithms are computationally expensive when the latent variables are high-dimensional and correlated, as is the case for latent Gaussian random field models. Latent Gaussian random field models are widely used, for example, in building flexible regression models and in the interpolation of spatially dependent data in many research areas such as analyzing count data in disease modeling and presence-absence satellite images of ice sheets. We propose a computationally efficient MCML algorithm by using a projection-based approach to reduce the dimensions of the random effects. We develop an iterative method for finding an effective importance function; this is generally a challenging problem and is crucial for the MCML algorithm to be computationally feasible. We find that our method is applicable to both continuous (latent Gaussian process) and discrete domain (latent Gaussian Markov random field) models. We illustrate the application of our methods to challenging simulated and real data examples for which maximum likelihood estimation would otherwise be very challenging. Furthermore, we study an often overlooked challenge in MCML approaches to latent variable models: practical issues in calculating standard errors of the resulting estimates, and assessing whether resulting confidence intervals provide nominal coverage. Our study therefore provides useful insights into the details of implementing MCML algorithms for high-dimensional latent variable models. Supplementary materials for this article are available online.

Texture Feature-Based Classification on Transrectal Ultrasound Image for Prostatic Cancer Detection.

Prostate cancer is one of the most common cancers in men. Early detection of prostate cancer is the key to successful treatment. Ultrasound imaging is one of the most suitable methods for the early detection of prostate cancer. Although ultrasound images can show cancer lesions, subjective interpretation is not accurate. Therefore, this paper proposes a transrectal ultrasound image analysis method, aiming at characterizing prostate tissue through image processing to evaluate the possibility of malignant tumours. Firstly, the input image is preprocessed by optical density conversion. Then, local binarization and Gaussian Markov random fields are used to extract texture features, and the linear combination is performed. Finally, the fused texture features are provided to SVM classifier for classification. The method has been applied to data set of 342 transrectal ultrasound images obtained from hospitals with an accuracy of 70.93%, sensitivity of 70.00%, and specificity of 71.74%. The experimental results show that it is possible to distinguish cancerous tissues from noncancerous tissues to some extent.

Adaptive volumetric texture segmentation based on Gaussian Markov random fields features

An adaptive method based on three dimensional Gaussian Markov Random fields (3D-GMRF) is proposed in this paper for volumetric texture segmentation. A feature vector is extracted for each voxel in a given volumetric texture image using an estimation cube. However, the selection of the size for this estimation cube causes some fundamental issues related to the uncertainty principle and the inability of the model to capture different texture patterns. These issues are tackled here by employing an adaptive method where the size of the estimation cube is adaptively varying to capture different patterns and also minimize the number of voxels that are related to different texture classes inside the estimation cube. The feature vectors that consist of the estimated parameters of the GMRF and form the parameter volume are hence employed to segment volumetric textures. These features are smoothed by applying an averaging filter using an adaptive averaging technique. Such an averaging filter improves the segmentation results considerably. Our method proposed here is evaluated on a synthetic volumetric texture dataset and compared with other methods to demonstrate the superiority of our segmentation method.

Bayesian estimation of multivariate Gaussian Markov random fields with constraint.

This article concerns with conditionally formulated multivariate Gaussian Markov random fields (MGMRF) for modeling multivariate local dependencies with unknown dependence parameters subject to positivity constraint. In the context of Bayesian hierarchical modeling of lattice data in general and Bayesian disease mapping in particular, analytic and simulation studies provide new insights into various approaches to posterior estimation of dependence parameters under "hard" or "soft" positivity constraint, including the well-known strictly diagonal dominance criterion and options of hierarchical priors. Hierarchical centering is examined as a means to gain computational efficiency in Bayesian estimation of multivariate generalized linear mixed effects models in the presence of spatial confounding and weakly identified model parameters. Simulated data on irregular or regular lattice, and three datasets from the multivariate and spatiotemporal disease mapping literature, are used for illustration. The present investigation also sheds light on the use of deviance information criterion for model comparison, choice, and interpretation in the context of posterior risk predictions judged by borrowing-information and bias-precision tradeoff. The article concludes with a summary discussion and directions of future work. Potential applications of MGMRF in spatial information fusion and image analysis are briefly mentioned.

Mobile Robotic Sensors for Environmental Monitoring using Gaussian Markov Random Field

SUMMARYThis paper addresses the issue of monitoring spatial environmental phenomena of interest utilizing information collected by a network of mobile, wireless, and noisy sensors that can take discrete measurements as they navigate through the environment. It is proposed to employ Gaussian Markov random field (GMRF) represented on an irregular discrete lattice by using the stochastic partial differential equations method to model the physical spatial field. It then derives a GMRF-based approach to effectively predict the field at unmeasured locations, given available observations, in both centralized and distributed manners. Furthermore, a novel but efficient optimality criterion is then proposed to design centralized and distributed adaptive sampling strategies for the mobile robotic sensors to find the most informative sampling paths in taking future measurements. By taking advantage of conditional independence property in the GMRF, the adaptive sampling optimization problem is proven to be resolved in a deterministic time. The effectiveness of the proposed approach is compared and demonstrated using pre-published data sets with appealing results.

Improved optical tomography based on hybrid frequency-domain and time-domain radiative transfer model

Based on the hybrid frequency-domain (FD) and time-domain (TD) radiative transfer equation (RTE), a novel reconstruction strategy is developed to retrieve the optical parameter fields in the participating medium. The discrete ordinate method is employed to solve the forward FD and TD RTE to simulate the radiative transfer process. The sequential quadratic programming is utilized to solve the inverse problem for obtaining the optical parameters combined with an adjoint method. The Otsu algorithm is applied to the FD reconstructed results to distinguish the target region and the background region. To overcome the ill-posedness of the inverse problem, the generalized Gaussian Markov random field model is employed as the regularization term in the objective function. Various numerical experiments are studied and all results demonstrate that the proposed hybrid reconstruction scheme is suitable for efficient and accurate optical tomography by combining the FD and TD radiative transfer models. Meanwhile, the crosstalk of the ill-posed inverse problem can be alleviated effectively.

Modeling spatial data using local likelihood estimation and a Matérn to spatial autoregressive translation

Modeling data with nonstationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a two‐stage approach to modeling nonstationary covariances that is efficient for large data sets. First, maximum likelihood estimation is used in local, moving windows to infer spatially varying covariance parameters. These surfaces of covariance parameters are then encoded into a global covariance model specifying the second‐order structure for the complete spatial domain. From this second step, the resulting global model allows for efficient simulation and prediction. This work uses a nonstationary spatial autoregressive (SAR) model, related to Gaussian Markov random field methods, as the global model which is amenable to plug in local estimates and practical for large datasets. A simulation study is used to establish the accuracy of local Matérn parameter estimation as a reliable technique for small window sizes and a modest number of replicated fields. This modeling approach is implemented on a nonstationary climate model dataset with the goal of emulating the variation in the numerical model ensemble using a Gaussian process.

Predictive Generalized Graph Fourier Transform for Attribute Compression of Dynamic Point Clouds

As 3D scanning devices and depth sensors advance, dynamic point clouds have attracted increasing attention as a format for 3D objects in motion, with applications in various fields such as immersive telepresence, navigation for autonomous driving and gaming. Nevertheless, the tremendous amount of data in dynamic point clouds significantly burden transmission and storage. To this end, we propose a complete compression framework for attributes of 3D dynamic point clouds, focusing on optimal inter-coding. Firstly, we derive the optimal inter-prediction and predictive transform coding assuming the Gaussian Markov Random Field model with respect to a spatio-temporal graph underlying the attributes of dynamic point clouds. The optimal predictive transform proves to be the Generalized Graph Fourier Transform in terms of spatio-temporal decorrelation. Secondly, we propose refined motion estimation via efficient registration prior to inter-prediction, which searches the temporal correspondence between adjacent frames of irregular point clouds. Finally, we present a complete framework based on the optimal inter-coding and our previously proposed intra-coding, where we determine the optimal coding mode from rate-distortion optimization with the proposed offline-trained λ-Q model. Experimental results show that we achieve around 17% bit rate reduction on average over competitive dynamic point cloud compression methods.