3D Markov Random Field Research Articles

Structured Hybrid Message Passing Based Channel Estimation for Massive MIMO-OFDM Systems

This paper investigates uplink channel estimation for massive multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with uniform planar array (UPA) antennas at the base station (BS). We first establish a triple beam-based channel model using sampled steering vectors. Based on the presented channel model, we further develop a three-dimensional (3D) Markov random field (MRF) probability model to capture the structured channel sparsity. Then constrained Bethe free energy (BFE) minimization is introduced to provide a systematic theoretical framework for message passing. Under this framework, we derive a structured hybrid message passing (SHMP) algorithm to address the channel estimation problem. The proposed algorithm can significantly improve the estimation accuracy by exploiting the clustered sparse structure of channels with low complexity. Moreover, aiming at the fine factors of the triple beam-based channel model and the coupling parameter of the 3D-MRF sparsity model, we analyze the effect of their different settings in the numerical simulation. Finally, extensive simulation results verify the superiority of the proposed SHMP algorithm.

Hyperspectral image classification with deep 3D capsule network and Markov random field

To address the existing problems of capsule networks in deep feature extraction and spatial-spectral feature fusion of hyperspectral images, this paper proposes a hyperspectral image classification method that combines a deep residual 3D capsule network and Markov random field. Based on this method, the deep spatial-spectral features of hyperspectral images are extracted using the deep residual 3D convolutional structure, the vector capsules of the features are obtained by the initial capsule layer and mapped into probability capsules via the 3D dynamic routing mechanism to construct the classification probability map, and the spatial structure of the classification results is regularised by the Markov random field to further improve the classification accuracy and performance of the images. Two sets of benchmark hyperspectral images, namely Indian Pines and Pavia University data sets, were used to conduct comparative experiments and ablation study. The experimental results showed that, compared with the conventional convolutional neural network and existing capsule network models, the proposed method not only improves the classification accuracy of the images but also partly eliminates the category noise and affords a more regular classification probability map.

A one-step Bayesian inversion framework for 3D reservoir characterization based on a Gaussian mixture model — A Norwegian Sea demonstration

We have developed a one-step approach for Bayesian prediction and uncertainty quantification of lithology/fluid classes, petrophysical properties, and elastic attributes conditional on prestack 3D seismic amplitude-variation-with-offset data. A 3D Markov random field prior model is assumed for the lithology/fluid classes to ensure spatially coupled lithology/fluid class predictions in the lateral and vertical directions. Conditional on the lithology/fluid classes, we consider Gauss-linear petrophysical and rock-physics models including depth trends. Then, the marginal prior models for the petrophysical properties and elastic attributes are multivariate Gaussian mixture models. The likelihood model is assumed to be Gauss-linear to allow for analytic computation. A recursive algorithm that translates the Gibbs formulation of the Markov random field into a set of vertical Markov chains is proposed. This algorithm provides a proposal density in a Markov chain Monte Carlo algorithm such that efficient simulation from the posterior model of interest in three dimensions is feasible. The model is demonstrated on real data from a Norwegian Sea gas reservoir. We evaluate the model at the location of a blind well, and we compare results from the proposed model with results from a set of 1D models in which each vertical trace is inverted independently. At the blind well location, we obtain at most a 60% reduction in the root-mean-square error for the proposed 3D model compared to the model without lateral spatial coupling.

Polarimetric SAR Image Semantic Segmentation With 3D Discrete Wavelet Transform and Markov Random Field

Polarimetric synthetic aperture radar (PolSAR) image segmentation is currently of great importance in image processing for remote sensing applications. However, it is a challenging task due to two main reasons. Firstly, the label information is difficult to acquire due to high annotation costs. Secondly, the speckle effect embedded in the PolSAR imaging process remarkably degrades the segmentation performance. To address these two issues, we present a contextual PolSAR image semantic segmentation method in this paper.With a newly defined channelwise consistent feature set as input, the three-dimensional discrete wavelet transform (3D-DWT) technique is employed to extract discriminative multi-scale features that are robust to speckle noise. Then Markov random field (MRF) is further applied to enforce label smoothness spatially during segmentation. By simultaneously utilizing 3D-DWT features and MRF priors for the first time, contextual information is fully integrated during the segmentation to ensure accurate and smooth segmentation. To demonstrate the effectiveness of the proposed method, we conduct extensive experiments on three real benchmark PolSAR image data sets. Experimental results indicate that the proposed method achieves promising segmentation accuracy and preferable spatial consistency using a minimal number of labeled pixels.

Polycrystalline Microstructure Reconstruction Using Markov Random Fields and Histogram Matching

A new numerical method is presented for reconstructing three-dimensional (3D) microstructures from two-dimensional (2D) sections, imaged on orthogonal planes, by exploiting the complete red–green–blue (RGB) color space. The algorithm reconstructs 3D models through sampling voxel neighborhoods to representative 2D micrographs, based upon a Markovian assumption. The sampling is followed by an optimization procedure, ensuring smoothness across the orthogonal sections of the synthesized voxels. Previous 3D Markov random field (MRF) microstructure reconstruction techniques were restricted to traditional grayscale images only. This method now enables the use of the entire RGB spectrum, employing a histogram matching step. This paper examines the algorithm’s accurate representation of orientations and morphologies, encompassing a variety of micrographs from electron backscatter diffraction (EBSD) and polarized light microscopy.

MRF model based real‐time traffic flow prediction with support vector regression

A novel statistical model for real-time traffic flow prediction is proposed. In this study, a 3D Markov random field (MRF) is used to model the temporal dynamics of the traffic flow measured by VDS sensor network. Then, the spatial and temporal relations between roads at a given location are represented by the 3D graph using cliques, then its structure is determined by clique parameters. Here, a support vector regression is adopted for estimating the correlation parameters. The technique is applied to actual traffic flow data from Gyeongbu expressway, South Korea. The experiments demonstrate that the proposed method can predict the traffic flow with an accuracy of 85.6%, which improves 17.3% of the existing state-of-the-art method.

A vessel segmentation method for multi-modality angiographic images based on multi-scale filtering and statistical models.

BackgroundAccurate segmentation of blood vessels plays an important role in the computer-aided diagnosis and interventional treatment of vascular diseases. The statistical method is an important component of effective vessel segmentation; however, several limitations discourage the segmentation effect, i.e., dependence of the image modality, uneven contrast media, bias field, and overlapping intensity distribution of the object and background. In addition, the mixture models of the statistical methods are constructed relaying on the characteristics of the image histograms. Thus, it is a challenging issue for the traditional methods to be available in vessel segmentation from multi-modality angiographic images.MethodsTo overcome these limitations, a flexible segmentation method with a fixed mixture model has been proposed for various angiography modalities. Our method mainly consists of three parts. Firstly, multi-scale filtering algorithm was used on the original images to enhance vessels and suppress noises. As a result, the filtered data achieved a new statistical characteristic. Secondly, a mixture model formed by three probabilistic distributions (two Exponential distributions and one Gaussian distribution) was built to fit the histogram curve of the filtered data, where the expectation maximization (EM) algorithm was used for parameters estimation. Finally, three-dimensional (3D) Markov random field (MRF) were employed to improve the accuracy of pixel-wise classification and posterior probability estimation. To quantitatively evaluate the performance of the proposed method, two phantoms simulating blood vessels with different tubular structures and noises have been devised. Meanwhile, four clinical angiographic data sets from different human organs have been used to qualitatively validate the method. To further test the performance, comparison tests between the proposed method and the traditional ones have been conducted on two different brain magnetic resonance angiography (MRA) data sets.ResultsThe results of the phantoms were satisfying, e.g., the noise was greatly suppressed, the percentages of the misclassified voxels, i.e., the segmentation error ratios, were no more than 0.3%, and the Dice similarity coefficients (DSCs) were above 94%. According to the opinions of clinical vascular specialists, the vessels in various data sets were extracted with high accuracy since complete vessel trees were extracted while lesser non-vessels and background were falsely classified as vessel. In the comparison experiments, the proposed method showed its superiority in accuracy and robustness for extracting vascular structures from multi-modality angiographic images with complicated background noises.ConclusionsThe experimental results demonstrated that our proposed method was available for various angiographic data. The main reason was that the constructed mixture probability model could unitarily classify vessel object from the multi-scale filtered data of various angiography images. The advantages of the proposed method lie in the following aspects: firstly, it can extract the vessels with poor angiography quality, since the multi-scale filtering algorithm can improve the vessel intensity in the circumstance such as uneven contrast media and bias field; secondly, it performed well for extracting the vessels in multi-modality angiographic images despite various signal-noises; and thirdly, it was implemented with better accuracy, and robustness than the traditional methods. Generally, these traits declare that the proposed method would have significant clinical application.

Cerebrovascular segmentation from TOF using stochastic models

In this paper, we present an automatic statistical approach for extracting 3D blood vessels from time-of-flight (TOF) magnetic resonance angiography (MRA) data. The voxels of the dataset are classified as either blood vessels or background noise. The observed volume data is modeled by two stochastic processes. The low level process characterizes the intensity distribution of the data, while the high level process characterizes their statistical dependence among neighboring voxels. The low level process of the background signal is modeled by a finite mixture of one Rayleigh and two normal distributions, while the blood vessels are modeled by one normal distribution. The parameters of the low level process are estimated using the expectation maximization (EM) algorithm. Since the convergence of the EM is sensitive to the initial estimate of the model parameters, an automatic method for parameter initialization, based on histogram analysis, is provided. To improve the quality of segmentation achieved by the proposed low level model especially in the regions of significantly vascular signal loss, the high level process is modeled as a Markov random field (MRF). Since MRF is sensitive to edges and the intracranial vessels represent roughly 5% of the intracranial volume, 2D MRF will destroy most of the small and medium sized vessels. Therefore, to reduce this limitation, we employed 3D MRF, whose parameters are estimated using the maximum pseudo likelihood estimator (MPLE), which converges to the true likelihood under large lattice. Our proposed model exhibits a good fit to the clinical data and is extensively tested on different synthetic vessel phantoms and several 2D/3D TOF datasets acquired from two different MRI scanners. Experimental results showed that the proposed model provides good quality of segmentation and is capable of delineating vessels down to 3 voxel diameters.

Recognition of lung nodule shadows from chest X‐ray CT images using 3D Markov random field models

AbstractThis paper presents a scheme for recognizing nodule shadows that are candidate lung cancer lesions from chest X‐ray CT images. In recognizing shadow candidates, their surrounding shadows give useful information. The proposed scheme recognizes nodule shadows by formulating the relationships between shadow candidates and their surrounding shadows in the framework of a three‐dimensional Markov random field model. First, it detects isolated shadows that become nodule candidates, extracts a volume of interest that includes shadow candidates, and divides the volume of interest into rectangular regions. It expresses nodules and blood vessels in three‐dimensional geometric models of spheres and cylinders, and lists a number of object models having high probabilities of existing in each rectangular region. It then generates a combination of object models by assembling the physical models. It formulates the relationships between each rectangular region, anatomical verifications of the object model combinations and the degree of agreement between observed CT images and object model combinations in the framework of a three‐dimensional Markov random field model, and computes the probability that a shadow candidate is a nodule and the probability that the shadow candidate is not a nodule. A shadow candidate is determined to be a nodule if the probability of it being a nodule is high, while it is determined to be normal otherwise. The proposed scheme is applied to actual CT images of 10‐mm slice intervals to show its efficacy. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(8): 82–95, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10453

Recognition of lung nodules from X-ray CT images using 3D MRF models

In this paper, we propose a new recognition method of lung nodules from X-ray CT images using 3D Markov random field (MRF) models with geometrical object models. Some results acquired by this method to actual CT images are shown.