Gaussian Markov Random Field Model Research Articles

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.

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

Reconstruction of optical parameter fields in graded refractive index media based on laser beam deflection and attenuation measurement.

Graded refractive index media (GRIM) are widely applied as special functional materials in many practical engineering fields. Accurate knowledge of the optical parameters is key to using GRIM. In this study, simultaneous reconstruction of the refractive index and absorption coefficient fields of GRIM based on laser beam deflection and attenuation measurement is studied. A set of rays from the given positions along the given directions transits GRIM, and the deflection and attenuation of rays at the exit boundary are recorded as measurement information. A two-step reconstruction strategy is proposed to reconstruct the refractive index and absorption coefficient fields. First, the refractive index field is reconstructed from the ray deflection measurement information. Then, the ray trajectory can be obtained by the Runge-Kutta ray tracing technique based on the reconstructed refractive index field. Afterwards, the absorption coefficient field is reconstructed from the ray attenuation measurement according to the Bouguer law. The regularization technique based on the generalized Gaussian Markov random field model is employed to improve the reconstruction results. All test results show that the two-step reconstruction strategy is accurate and can be regarded as a promising reconstruction technique.

Seasonal Habitat Selection by American White Pelicans

Resource utilization strategies of avian migrants are a major concern for conservation and management. Understanding seasonal habitat selection by migratory birds helps us explain the ongoing continental declines of migratory bird populations. Our objective was to compare the second-order and third-order habitat selection by the American White Pelican (Pelecanus erythrorhynchos; hereafter pelican) between the breeding and non-breeding grounds. We tested the Lack hypothesis that habitat selection by migratory birds is stronger on the breeding grounds than on the non-breeding grounds. We used random-effect Dirichlet-multinomial models to estimate the second-order habitat selection between the seasons with the GPS locations of 32 tracked pelicans. We used Gaussian Markov random field models to estimate the third-order habitat selection by pelicans at the breeding and non-breeding grounds, accounting for spatial autocorrelation. Pelicans strongly selected waterbodies and wetlands at both non-breeding and breeding grounds, tracking their foraging habitats between the seasons at the home range level. However, pelicans exhibited seasonal differences in the strength of the third-order selection of wetlands and waterbodies with foraging habitat selection being stronger at the breeding grounds than at the non-breeding grounds, supporting the Lack hypothesis.

Fitting double hierarchical models with the integrated nested Laplace approximation

Double hierarchical generalized linear models (DHGLM) are a family of models that are flexible enough as to model hierarchically the mean and scale parameters. In a Bayesian framework, fitting highly parameterized hierarchical models is challenging when this problem is addressed using typical Markov chain Monte Carlo (MCMC) methods due to the potential high correlation between different parameters and effects in the model. The integrated nested Laplace approximation (INLA) could be considered instead to avoid dealing with these problems. However, DHGLM do not fit within the latent Gaussian Markov random field (GMRF) models that INLA can fit. In this paper, we show how to fit DHGLM with INLA by combining INLA and importance sampling (IS) algorithms. In particular, we will illustrate how to split DHGLM into submodels that can be fitted with INLA so that the remainder of the parameters are fit using adaptive multiple IS (AMIS) with the aid of the graphical representation of the hierarchical model. This is illustrated using a simulation study on three different types of models and two real data examples.

Modelling spatial dependence for Loss Given Default in peer-to-peer lending

We propose estimating a model for Loss Given Default (LGD) that allows accounting for spatial dependence between peer-to-peer (P2P) loans. We suggest the LGD two-stage approach with the Gaussian Markov Random Field model in each stage to represent the spatial variations. In the first stage, we predict total loss and no loss using two binary additive models with a flexible parametric link function given by the Generalised Extreme Value (GEV) distribution. In the second stage, we consider a beta regression in the Generalised Additive Model for Location Scale and Shape (GAMLSS) framework. The main advantage of our proposal is to provide accurate calibrated region-specific LGD estimates. We apply this model to a comprehensive dataset on P2P loans provided by Lending Club. The GEV link function better fits the data than the logit function in the first stage. The most important finding for financial institutions’ risk assessment is that including spatial effects and using a two-stage approach provide conservative estimates of the expected shortfall.

Satellite Image Retrieval Based on Adaptive Gaussian Markov Random Field Model with Bayes Back-Propagation Neural Network

Satellite Image Retrieval Based on Adaptive Gaussian Markov Random Field Model with Bayes Back-Propagation Neural Network

Fast and flexible estimation of effective migration surfaces.

Spatial population genetic data often exhibits 'isolation-by-distance,' where genetic similarity tends to decrease as individuals become more geographically distant. The rate at which genetic similarity decays with distance is often spatially heterogeneous due to variable population processes like genetic drift, gene flow, and natural selection. Petkova et al., 2016 developed a statistical method called Estimating Effective Migration Surfaces (EEMS) for visualizing spatially heterogeneous isolation-by-distance on a geographic map. While EEMS is a powerful tool for depicting spatial population structure, it can suffer from slow runtimes. Here, we develop a related method called Fast Estimation of Effective Migration Surfaces (FEEMS). FEEMS uses a Gaussian Markov Random Field model in a penalized likelihood framework that allows for efficient optimization and output of effective migration surfaces. Further, the efficient optimization facilitates the inference of migration parameters per edge in the graph, rather than per node (as in EEMS). With simulations, we show conditions under which FEEMS can accurately recover effective migration surfaces with complex gene-flow histories, including those with anisotropy. We apply FEEMS to population genetic data from North American gray wolves and show it performs favorably in comparison to EEMS, with solutions obtained orders of magnitude faster. Overall, FEEMS expands the ability of users to quickly visualize and interpret spatial structure in their data.

Spatial modelling of risk premiums for water damage insurance

In this paper, we compare different spatial models for modelling the risk premium for water damage insurance on the level of the policyholder. We evaluate four models that take the spatial variability into account: (1) the Intrinsic Conditional Auto-Regressive (ICAR) model; (2) the Besag, York, Mollier (BYM) model; (3) the independent random effects model; and (4) a spatial spline model. The models are compared on a huge data set from the Norwegian insurance company Gjensidige containing seven million observations of policyholders during the period 2011–2018. While Bayesian methods are most frequently used for inference in Gaussian Markov Random Field models, we take a frequentist approach and estimate the model parameters using Laplace approximated restricted maximum likelihood. Using the R package mgcv, we compare the different models for claim frequency, claim size and combined in a risk premium model in a comprehensive cross-validation study. Practical measures such as the loss ratio lift, double lift and Gini index are used to compare performance. Finally, we also compare mgcv with INLA and show that for reasonable big data sets we get identical estimates at a much lower computational cost.

Robust depth map inpainting using superpixels and non-local Gauss–Markov random field prior

Depth maps contain 3D geometrical information of a scene which can be useful in many applications. In this work we address the task of inpainting a depth map afflicted by regions with missing data. Initially, we inpaint depth values missing at random locations as well as due to overlaid text. Subsequently, we propose an approach for filling large holes in the input depth map wherein superpixel division of the corresponding RGB image is also exploited. We use a non-local extension of the classical Gauss–Markov random field model for the completed depth map, so that missing information in the degraded observation can be estimated depending upon self-similarities between non-local patches inside a superpixel based search window. Several experiments performed with disparity maps and real world depth data exhibit the efficacy of the proposed algorithm.

Combining heterogeneous spatial datasets with process-based spatial fusion models: A unifying framework

In modern spatial statistics, the structure of data has become more heterogeneous. Depending on the types of spatial data, different modeling strategies are used. For example, kriging approaches for geostatistical data; Gaussian Markov random field models for lattice data; or log Gaussian Cox process models for point-pattern data. Despite these different modeling choices, the nature of underlying data-generating (latent) processes is often the same, which can be represented by some continuous spatial surfaces. A unifying framework is introduced for process-based multivariate spatial fusion models. The framework can jointly analyze all three aforementioned types of spatial data or any combinations thereof. Moreover, the framework accommodates different likelihoods for geostatistical and lattice data. It is shown that some established approaches, such as linear models of coregionalization, can be viewed as special cases of the proposed framework. A flexible and scalable implementation using R-INLA is provided. Simulation studies confirm that the prediction of latent processes improves as one moves from univariate spatial models to multivariate spatial fusion models. The framework is illustrated via a case study using datasets from a cross-sectional study linked with a national cohort in Switzerland. The differences in underlying spatial risks between respiratory disease and lung cancer are examined in the case study.

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.

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.

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.

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.

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.

Image Steganography With Symmetric Embedding Using Gaussian Markov Random Field Model

Recent advances on adaptive steganography show that the performance of image steganographic communication can be improved by incorporating the non-additive models that capture the dependencies among adjacent pixels. In this paper, a Gaussian Markov Random Field model (GMRF) with four-element cross neighborhood is proposed to characterize the interactions among local elements of cover images, and the problem of secure image steganography is formulated as the one of minimization of KL-divergence in terms of a series of low-dimensional clique structures associated with GMRF by taking advantages of the conditional independence of GMRF. The adoption of the proposed GMRF tessellates the cover image into two disjoint subimages, and an alternating iterative optimization scheme is developed to effectively embed the given payload while minimizing the total KL-divergence between cover and stego, i.e., the statistical detectability. Experimental results demonstrate that the proposed GMRF outperforms the prior arts of model based schemes, e.g., MiPOD, and rivals the state-of-the-art HiLL for practical steganography, where the selection channel knowledges are unavailable to steganalyzers.

Graph-based Transforms for Video Coding.

In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of transforms called graph-based transforms (GBTs) for video compression, and proposes two different techniques to design GBTs. In the first technique, we formulate an optimization problem to learn graphs from data and provide solutions for optimal separable and nonseparable GBT designs, called GL-GBTs. The optimality of the proposed GL-GBTs is also theoretically analyzed based on Gaussian-Markov random field (GMRF) models for intra and inter predicted block signals. The second technique develops edge-adaptive GBTs (EA-GBTs) in order to flexibly adapt transforms to block signals with image edges (discontinuities). The advantages of EA-GBTs are both theoretically and empirically demonstrated. Our experimental results show that the proposed transforms can significantly outperform the traditional Karhunen-Loeve transform (KLT).

Information-Based Hierarchical Planning for a Mobile Sensing Network in Environmental Mapping

This article investigates the problem of information-based sampling design and path planning for a mobile sensing network to predict scalar fields of monitored environments. A hierarchical framework with a built-in Gaussian Markov random field model is proposed to provide adaptive sampling for efficient field reconstruction. In the proposed framework, a nonmyopic planner is operated at a sink to navigate the mobile sensing agents in the field to the sites that are most informative. Meanwhile, a myopic planner is carried out on board each agent. A tradeoff between computationally intensive global optimization and efficient local greedy search is incorporated into the system. The mobile sensing agents can be scheduled online through an anytime algorithm to visit and observe the high-information sites. Experiments on both synthetic and real-world datasets are used to demonstrate the feasibility and efficiency of the proposed planner in model exploitation and adaptive sampling for environmental field mapping.

Automated framework for accurate segmentation of leaf images for plant health assessment.

Leaf segmentation is significantly important in assisting ecologists to automatically detect symptoms of disease and other stressors affecting trees. This paper employs state-of-the-art techniques in image processing to introduce an accurate framework for segmenting leaves and diseased leaf spots from images. The proposed framework integrates an appearance model that visually represents the current input image with the color prior information generated from RGB color images that were formerly saved in our database. Our framework consists of four main steps: (1) Enhancing the accuracy of the segmentation at minimum time by making use of contrast changes to automatically identify the region of interest (ROI) of the entire leaf, where the pixel-wise intensity relations are described by an electric field energy model. (2) Modeling the visual appearance of the input image using a linear combination of discrete Gaussians (LCDG) to predict the marginal probability distributions of the grayscale ROI main three classes. (3) Calculating the pixel-wise probabilities of these three classes for the color ROI based on the color prior information of database images that are segmented manually, where the current and prior pixel-wise probabilities are used to find the initial labels. (4) Refining the labels with the generalized Gauss-Markov random field model (GGMRF), which maintains the continuity. The proposed segmentation approach was applied to the leaves of mangrove trees in Abu Dhabi in the United Arab Emirates. Experimental validation showed high accuracy, with a Dice similarity coefficient 90% for distinguishing leaf spot from healthy leaf area.