Hidden Markov Random Field Model Research Articles

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.

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

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.

Exploring drought-responsive crucial genes in Sorghum

Drought severely affects global food production. Sorghum is a typical drought-resistant model crop. Based on RNA-seq data for Sorghum with multiple time points and the gray correlation coefficient, this paper firstly selects candidate genes via mean variance test and constructs weighted gene differential co-expression networks (WGDCNs); then, based on guilt-by-rewiring principle, the WGDCNs and the hidden Markov random field model, drought-responsive crucial genes are identified for five developmental stages respectively. Enrichment and sequence alignment analysis reveal that the screened genes may play critical functional roles in drought responsiveness. A multilayer differential co-expression network for the screened genes reveals that Sorghum is very sensitive to pre-flowering drought. Furthermore, a crucial gene regulatory module is established, which regulates drought responsiveness via plant hormone signal transduction, MAPK cascades, and transcriptional regulations. The proposed method can well excavate crucial genes through RNA-seq data, which have implications in breeding of new varieties with improved drought tolerance.

HMRFS–TP: long-term daily gap-free snow cover products over the Tibetan Plateau from 2002 to 2021 based on hidden Markov random field model

Abstract. Snow cover plays an essential role in climate change and the hydrological cycle of the Tibetan Plateau. The widely used Moderate Resolution Imaging Spectroradiometer (MODIS) snow products have two major issues: massive data gaps due to frequent clouds and relatively low estimate accuracy of snow cover due to complex terrain in this region. Here we generate long-term daily gap-free snow cover products over the Tibetan Plateau at 500 m resolution by applying a hidden Markov random field (HMRF) technique to the original MODIS snow products over the past two decades. The data gaps of the original MODIS snow products were fully filled by optimally integrating spectral, spatiotemporal, and environmental information within HMRF framework. The snow cover estimate accuracy was greatly increased by incorporating the spatiotemporal variations of solar radiation due to surface topography and sun elevation angle as the environmental contextual information in HMRF-based snow cover estimation. We evaluated our snow products, and the accuracy is 98.29 % in comparison with in situ observations, and 91.36 % in comparison with high-resolution snow maps derived from Landsat images. Our evaluation also suggests that the incorporation of spatiotemporal solar radiation as the environmental contextual information in HMRF modeling, instead of the simple use of surface elevation as the environmental contextual information, results in the accuracy of the snow products increases by 2.71 % and the omission error decreases by 3.59 %. The accuracy of our snow products is especially improved during snow transitional period, and over complex terrains with high elevation and sunny slopes. The new products can provide long-term and spatiotemporally continuous information of snow cover distribution, which is critical for understanding the processes of snow accumulation and melting, analyzing its impact on climate change, and facilitating water resource management in Tibetan Plateau. This dataset can be freely accessed from the National Tibetan Plateau Data Center at https://doi.org/10.11888/Cryos.tpdc.272204 (Huang and Xu, 2022).

Analyzing Spatial Transcriptomics Data Using Giotto.

Spatial transcriptomic technologies have been developed rapidly in recent years. The addition of spatial context to expression data holds the potential to revolutionize many fields in biology. However, the lack of computational tools remains a bottleneck that is preventing the broader utilization of these technologies. Recently, we have developed Giotto as a comprehensive, generally applicable, and user-friendly toolbox for spatial transcriptomic data analysis and visualization. Giotto implements a rich set of algorithms to enable robust spatial data analysis. To help users get familiar with the Giotto environment and apply it effectively in analyzing new datasets, we will describe the detailed protocols for applying Giotto without any advanced programming skills. © 2022 Wiley Periodicals LLC. Basic Protocol 1: Getting Giotto set up for use Basic Protocol 2: Pre-processing Basic Protocol 3: Clustering and cell-type identification Basic Protocol 4: Cell-type enrichment and deconvolution analyses Basic Protocol 5: Spatial structure analysis tools Basic Protocol 6: Spatial domain detection by using a hidden Markov random field model Support Protocol 1: Spatial proximity-associated cell-cell interactions Support Protocol 2: Assembly of a registered 3D Giotto object from 2D slices.

Joint dimension reduction and clustering analysis of single-cell RNA-seq and spatial transcriptomics data.

Dimension reduction and (spatial) clustering is usually performed sequentially; however, the low-dimensional embeddings estimated in the dimension-reduction step may not be relevant to the class labels inferred in the clustering step. We therefore developed a computation method, Dimension-Reduction Spatial-Clustering (DR-SC), that can simultaneously perform dimension reduction and (spatial) clustering within a unified framework. Joint analysis by DR-SC produces accurate (spatial) clustering results and ensures the effective extraction of biologically informative low-dimensional features. DR-SC is applicable to spatial clustering in spatial transcriptomics that characterizes the spatial organization of the tissue by segregating it into multiple tissue structures. Here, DR-SC relies on a latent hidden Markov random field model to encourage the spatial smoothness of the detected spatial cluster boundaries. Underlying DR-SC is an efficient expectation-maximization algorithm based on an iterative conditional mode. As such, DR-SC is scalable to large sample sizes and can optimize the spatial smoothness parameter in a data-driven manner. With comprehensive simulations and real data applications, we show that DR-SC outperforms existing clustering and spatial clustering methods: it extracts more biologically relevant features than conventional dimension reduction methods, improves clustering performance, and offers improved trajectory inference and visualization for downstream trajectory inference analyses.

Multi-Agent Reinforcement Learning with Optimal Equivalent Action of Neighborhood

In a multi-agent system, the complex interaction among agents is one of the difficulties in making the optimal decision. This paper proposes a new action value function and a learning mechanism based on the optimal equivalent action of the neighborhood (OEAN) of a multi-agent system, in order to obtain the optimal decision from the agents. In the new Q-value function, the OEAN is used to depict the equivalent interaction between the current agent and the others. To deal with the non-stationary environment when agents act, the OEAN of the current agent is inferred simultaneously by the maximum a posteriori based on the hidden Markov random field model. The convergence property of the proposed methodology proved that the Q-value function can approach the global Nash equilibrium value using the iteration mechanism. The effectiveness of the method is verified by the case study of the top-coal caving. The experiment results show that the OEAN can reduce the complexity of the agents’ interaction description, meanwhile, the top-coal caving performance can be improved significantly.

A hybrid framework for brain tissue segmentation in magnetic resonance images

AbstractHaving a robust image segmentation strategy is very important in magnetic resonance image (MRI) processing for an effective and early disease detection and diagnosis. Since MRI can present tissues of interest in both morphological and functional images, various segmentation techniques have been employed for this. The algorithms based on Markov random field (MRF) have shown strong abilities in dealing with noisy image segmentation compared to other methods. In this article, inspired by the random drift particle swarm optimization (RDPSO) algorithm, we propose a novel hybrid framework based on a combination of the RDPSO with the hidden MRF model and the expectation–maximization algorithm (HMRF‐EM), to be used for MRI segmentation in real‐time environments. The proposed hybrid framework is compared with the standalone HMRF‐EM method, two other MRF‐based stochastic relaxation algorithms, and two widely used brain tissue segmentation toolboxes on both simulated and real MRI datasets. The experimental results prove that the proposed hybrid framework can obtain better segmentation results than most of its competitors and has faster convergence speed than the compared stochastic optimization algorithms.

Semantic segmentation of cerebrospinal fluid and brain volume with a convolutional neural network in pediatric hydrocephalus\u2014transfer learning from existing algorithms

BackgroundFor the segmentation of medical imaging data, a multitude of precise but very specific algorithms exist. In previous studies, we investigated the possibility of segmenting MRI data to determine cerebrospinal fluid and brain volume using a classical machine learning algorithm. It demonstrated good clinical usability and a very accurate correlation of the volumes to the single area determination in a reproducible axial layer. This study aims to investigate whether these established segmentation algorithms can be transferred to new, more generalizable deep learning algorithms employing an extended transfer learning procedure and whether medically meaningful segmentation is possible.MethodsNinety-five routinely performed true FISP MRI sequences were retrospectively analyzed in 43 patients with pediatric hydrocephalus. Using a freely available and clinically established segmentation algorithm based on a hidden Markov random field model, four classes of segmentation (brain, cerebrospinal fluid (CSF), background, and tissue) were generated. Fifty-nine randomly selected data sets (10,432 slices) were used as a training data set. Images were augmented for contrast, brightness, and random left/right and X/Y translation. A convolutional neural network (CNN) for semantic image segmentation composed of an encoder and corresponding decoder subnetwork was set up. The network was pre-initialized with layers and weights from a pre-trained VGG 16 model. Following the network was trained with the labeled image data set. A validation data set of 18 scans (3289 slices) was used to monitor the performance as the deep CNN trained. The classification results were tested on 18 randomly allocated labeled data sets (3319 slices) and on a T2-weighted BrainWeb data set with known ground truth.ResultsThe segmentation of clinical test data provided reliable results (global accuracy 0.90, Dice coefficient 0.86), while the CNN segmentation of data from the BrainWeb data set showed comparable results (global accuracy 0.89, Dice coefficient 0.84). The segmentation of the BrainWeb data set with the classical FAST algorithm produced consistent findings (global accuracy 0.90, Dice coefficient 0.87). Likewise, the area development of brain and CSF in the long-term clinical course of three patients was presented.ConclusionUsing the presented methods, we showed that conventional segmentation algorithms can be transferred to new advances in deep learning with comparable accuracy, generating a large number of training data sets with relatively little effort. A clinically meaningful segmentation possibility was demonstrated.

Magnetic resonance imaging evaluation of vertebral tumor prediction using hierarchical hidden Markov random field model on Internet of Medical Things (IOMT) platform

Abstract Recently, prediction evaluation of the metastatic spine tumors in therapy is considered a significant area of research. Further, for spinal clinical diagnoses, a large amount of image data from different modalities is often used and interchangeably analyzed based on the automatic vertebra identification. It includes recognition of vertebral positions and recognition in several image modalities. Due to the differences in MR or CT images appearance or shape/size of the vertebras, the identification is however difficult in the present conventional medical research. The segmentation of vertebral tumors that are manually performed by MRI is an important and time-consuming process by the conventional research algorithms. The accuracy of identification of the size and location of spine tumors plays a major role in effective tumor diagnosis and treatment. Therefore, this paper presents the Hierarchical Hidden Markov Random Field Model (HHMRF) to predict the vertebral tumor for the early detection and diagnosis treatment in an effective and efficient manner. The importance of this research is to implement a state-of-the-art strategy for detection of tumors using HHMRF and threshold techniques in MRI images on the Internet of Medical Things Platform (IoMT). HHMRF can coordinate the final section of vertebral tumor homogeneous areas of tissue while preserving the edges between different tissue constituents more effectively using mathematical computation. The proposed method attains the state-of-the-art performance on the diagnosis and segmentation of lumbar spinal stenosis using deep neural network and experimentally analyzed with 97.44% accuracy and 97.11% efficiency ratio on IoMT platform whereas proposed HHMRF achieves 98.5% high precision ratio compared to other existing TDCN (78.2%), DLA (81.6%), M-CNN (78.9%), and DCE-MRI (80.2%) methods.

Unsupervised Cerebrovascular Segmentation of TOF-MRA Images Based on Deep Neural Network and Hidden Markov Random Field Model.

Automated cerebrovascular segmentation of time-of-flight magnetic resonance angiography (TOF-MRA) images is an important technique, which can be used to diagnose abnormalities in the cerebrovascular system, such as vascular stenosis and malformation. Automated cerebrovascular segmentation can direct show the shape, direction and distribution of blood vessels. Although deep neural network (DNN)-based cerebrovascular segmentation methods have shown to yield outstanding performance, they are limited by their dependence on huge training dataset. In this paper, we propose an unsupervised cerebrovascular segmentation method of TOF-MRA images based on DNN and hidden Markov random field (HMRF) model. Our DNN-based cerebrovascular segmentation model is trained by the labeling of HMRF rather than manual annotations. The proposed method was trained and tested using 100 TOF-MRA images. The results were evaluated using the dice similarity coefficient (DSC), which reached a value of 0.79. The trained model achieved better performance than that of the traditional HMRF-based cerebrovascular segmentation method in binary pixel-classification. This paper combines the advantages of both DNN and HMRF to train the model with a not so large amount of the annotations in deep learning, which leads to a more effective cerebrovascular segmentation method.

Hidden Markov Random Field for Multi-Agent Optimal Decision in Top-Coal Caving

Applying model-based learning for the optimal decision of the multi-agent system is not trivial due to the expensive price or even the impossibility of obtaining the ground truth for training the model of the complex environment. Such as learning the optimal action of hydraulic supports in the top-coal caving, the optimal action could not accessible as the ground truth of the corresponding state in the intricate processes. Regarding the latent ground truth as the hidden variable is an effective method in the hidden Markov model. This paper extends the hidden variable of ground truth to the multi-agent system and proposes the hidden Markov random field (HMRF) model with reinforcement learning for optimizing the action decision of the multi-agent. In the HMRF model, the input states and the output actions of the multi-agent are considered as an observable random field and a latent Markov random field, respectively. Based on the HMRF model, the optimal decision is inferred by the maximum posterior probability with the prior probability obtained by Q-learning. Meanwhile, the parameters of the HMRF model are estimated by the expectation maximum algorithm. In the experiment, the top-coal caving demonstrates the effectiveness of the proposed method that the recall of top-coal is improved prominently with a very small price of increasing the rock-rate. Furthermore, the proposed method is employed to deal with the predator-preys problem in the gym. The experiment result shows that the communication between agents by the HMRF increases the reward of the preys.

Segmentation of MR Brain Images Through Hidden Markov Random Field and Hybrid Metaheuristic Algorithm.

Image segmentation is one of the most critical tasks in Magnetic Resonance (MR) images analysis. Since the performance of most current image segmentation methods is suffered by noise and intensity non-uniformity artifact (INU), a precise and artifact resistant method is desired. In this work, we propose a new segmentation method combining a new Hidden Markov Random Field (HMRF) model and a novel hybrid metaheuristic method based on Cuckoo search (CS) and Particle swarm optimization algorithms (PSO). The new model uses adaptive parameters to allow balancing between the segmented components of the model. In addition, to improve the quality of searching solutions in the Maximum a posteriori (MAP) estimation of the HMRF model, the hybrid metaheuristic algorithm is introduced. This algorithm takes into account both the advantages of CS and PSO algorithms in searching ability by cooperating them with the same population in a parallel way and with a solution selection mechanism. Since CS and PSO are performing exploration and exploitation in the search space, respectively, hybridizing them in an intelligent way can provide better solutions in terms of quality. Furthermore, initialization of the population is carefully taken into account to improve the performance of the proposed method. The whole algorithm is evaluated on benchmark images including both the simulated and real MR brain images. Experimental results show that the proposed method can achieve satisfactory performance for images with noise and intensity inhomogeneity, and provides better results than its considered competitors.

A Spatially Constrained Probabilistic Model for Robust Image Segmentation.

In general, the hidden Markov random field (HMRF) represents the class label distribution of an image in probabilistic model based segmentation. The class label distributions provided by existing HMRF models consider either the number of neighboring pixels with similar class labels or the spatial distance of neighboring pixels with dissimilar class labels. Also, this spatial information is only considered for estimation of class labels of the image pixels, while its contribution in parameter estimation is completely ignored. This, in turn, deteriorates the parameter estimation, resulting in sub-optimal segmentation performance. Moreover, the existing models assign equal weightage to the spatial information for class label estimation of all pixels throughout the image, which, create significant misclassification for the pixels in boundary region of image classes. In this regard, the paper develops a new clique potential function and a new class label distribution, incorporating the information of image class parameters. Unlike existing HMRF model based segmentation techniques, the proposed framework introduces a new scaling parameter that adaptively measures the contribution of spatial information for class label estimation of image pixels. The importance of the proposed framework is depicted by modifying the HMRF based segmentation methods. The advantage of proposed class label distribution is also demonstrated irrespective of the underlying intensity distributions. The comparative performance of the proposed and existing class label distributions in HMRF model is demonstrated both qualitatively and quantitatively for brain MR image segmentation, HEp-2 cell delineation, natural image and object segmentation.

A High-Throughput Phenotyping Pipeline for Image Processing and Functional Growth Curve Analysis.

High-throughput phenotyping system has become more and more popular in plant science research. The data analysis for such a system typically involves two steps: plant feature extraction through image processing and statistical analysis for the extracted features. The current approach is to perform those two steps on different platforms. We develop the package “implant” in R for both robust feature extraction and functional data analysis. For image processing, the “implant” package provides methods including thresholding, hidden Markov random field model, and morphological operations. For statistical analysis, this package can produce nonparametric curve fitting with its confidence region for plant growth. A functional ANOVA model to test for the treatment and genotype effects on the plant growth dynamics is also provided.

Hidden Markov random field models applied to color homogeneity evaluation in dyed textile images

AbstractColor is one of the most important features in any textile material. Due to its competitive price, most of the colorants currently used for textile dyeing are synthetic, originated from nonrenewable sources, and highly pollutant. There is an increasing interest for natural processes to dye fabrics. When new textile dyeing technologies are developed, evaluating the quality of these techniques involves measuring the resulting color homogeneity using digital images. The presence of a texture effect, caused by the interlacing of warp and weft yarns, as well as small displacement of the fabric, creates a sophisticated dependence structure in pixels coloring. A random effects model is employed in order to separate the signal from the dyeing effect (fixed effect described by smooth functions) and warp and weft texture effect (Gaussian mixture driven by a hidden Markov random field), allowing an evaluation of color homogeneity in dyed textiles regardless of the effect of the texture.

A Superpixel-Based Coastline Extraction Algorithm for Single-Polarized ENVISAT and ERS Imagery

In single-polarization synthetic aperture radar imagery, coastline extraction is a challenging task due to complex coastal region condition, low incidence angles (<30°), VV or HH polarization, speckle and sea wind, which have to be handled by visual inspection and manual operation for coastline extraction. To solve this problem, this article proposes a coastline extraction algorithm by utilizing superpixel as the basic unit. An improved line finder is presented and involved in the simple linear iterative clustering to obtain better results around the dam. Then, Gabor feature is extracted to characterize the superpixels. Finally, the hidden Markov random field model is utilized to classify superpixels. A coarse to fine strategy is utilized to extract coastline for the experimental imagery. Four VV polarization ENVISAT and ERS images with incidence angle (30.9°−36.6°, 17°−42°, 17°−42°, 19°−26°) are used as the experimental imagery. Four sites in each imagery are chosen to evaluate the performance of proposed superpixel-based algorithm under the condition of complex coastal region such as a thin dam, sharp corner, weak boundary, together with low-to-moderate sea wind. By using the manually traced coastlines as the standards in the qualitative evaluations with the extracted results, with mean offset (MO) in pixels, root-mean-square error (RMSE) in pixels, proportion of overlapped pixels (OLP) in percentage, distance within one pixel (WOP) in percentage, and distance within two pixels (WTP) in percentage as performance comparison, the accuracy improvements in detecting coastline along the dam are at least about 0.08, 0.19, 2.07% in MO, RMSE, and OLP. The accuracy improvements of the sharp corner are at least about 0.07, 0.09, 2.44%, 2.69%, and 2.77%. The accuracy improvements of the weak boundary are about 2.63, 2.99, 5.26%, 11.46%, and 13.96%. While the proposed algorithm shows weaknesses with the comparison algorithms in WOP, WTP for the dam, OLP, WOP, and WTP for sea wind. In addition, the processing time of the proposed algorithm is a burden to obtain better accuracy performance. Experimental results show that the proposed coastline extraction algorithm is more effective and suitable for coastline extraction in comparison with other existing algorithms in the dam, weak boundary, and sharp corner.

From yield history to productivity zone identification with hidden Markov random fields

Modern precision agriculture equipment enables site-specific management by allowing different treatments for different parts of a field. This ability to subdivide the field calls for identifying management zones. A compromise between treating a field uniformly and treating every plant individually is needed, as the former does not maximize yields and the latter is often impractical. This work presents an algorithm for inferring the yield productivity zones (YPZ) for a field based on yield data from multiple years. The algorithm uses a hidden Markov random field model (HMRF) to find regions of the field which likely correspond to the same underlying yield distribution (i.e., productivity zones). These regions are modeled to be the same every year, but their distributions (i.e., yield characteristics) are allowed to vary with time to account for year-to-year variability (from e.g., weather effects, differing crops or crop varieties). The zone assignments and distributions are estimated using stochastic expectation maximization (SEM) and the maximizer of the posterior marginals (MPM). The underlying assumption of the model and algorithm is that the yields corresponding to a given YPZ will behave similarly and therefore derive from the same probability distribution. YPZs are useful inputs for determining management zones. An advantage of this method is that it is able to run with only the yield data which are automatically collected during harvest. Also, this method requires no crop specific calibration or configuration or normalization of the data by year.

A Realtime Algorithm for Distinguish Obstacle from Accessible Area in 3D Scene

A learning algorithm based on Hidden Markov random field model is designed, and three-dimensional data is extracted, and the robot is used as an experimental platform. In the process of recognition, obstacle areas and feasible areas are distinguished by template matching, and the accessible areas and obstacle areas of the scene around the robot are obtained by classification results. According to the state of the robot itself, the position and direction vectors of the robot are calculated. The robot adjusts its attitude under the control of the output vector, so as to avoid obstacles and move to the target point. Finally, it is proved that the experiment has ideal real-time performance, so it has an extensive practical application foundation.