Markov Random Field Parameters Research Articles

Stochastic stratigraphic modeling using Bayesian machine learning

Stratigraphic modeling with quantified uncertainty is an open question in engineering geology. In this study, a novel stratigraphic stochastic simulation approach is developed by integrating a Markov random field (MRF) model and a discriminant adaptive nearest neighbor-based k-harmonic mean distance (DANN-KHMD) classifier into a Bayesian framework. The DANN-KHMD classifier is effective for extracting anisotropic patterns from sparse and heterogeneous spatial categorical data such as borehole logs. The MRF parameters can be initially estimated roughly or customized (if site-specific knowledge is available). Later these parameters can be updated and regularized in an unsupervised manner with constraints from site exploration results in a Bayesian manner. Throughout the learning process, both the soil profile and the MRF parameters are updated in a probabilistic manner. The advantages of the proposed approach can be summarized into four points: 1) inferring stratigraphic profile and associated uncertainty in an automatic and fully unsupervised manner; 2) reasonable initial stratigraphic configurations can be sampled and hence lower the computational cost; 3) both stratigraphic uncertainty and model uncertainty are taken into consideration throughout the inferential process; 4) relying on no training stratigraphy images. To illustrate the effectiveness of the developed approach, two synthetic cases and three real-world cases are studied and the advantages of the new approach over existing approaches are demonstrated.

Segmentasi Citra Kanker Serviks Menggunakan Markov Random Field dan Algoritma K-Means

Cervical cancer is a dangerous disease caused by malignant tumors that grow on the cervix and has globally attacked many women. Pap smear test is one of the early prevention efforts for cervical cancer. Medical personnel often have difficulty identifying images of cervical cancer cells. Several studies have used the K-Means clustering method to identify cervical cancer cell images from Herlev dataset. This study uses the Herlev dataset with the K-Means clustering algorithm and also used the Markov Random Field parameter as a feature for the process of identifying cervical cancer cell images. This study compared the results of the proposed method with some differences in the preprocessing process. The experimental results show an accuracy of 74,51% for RGB channels without low pass filter. Accuracy of 75,11% is obtained from the segmentation process using RGB channels with low pass filter. A further increase in accuracy was obtained by 75,76% when the segmentation process used the grayscale channel with low pass Filter. Based on the segmentation experiment with the highest segmentation accuracy results, the classification process using K-Nearest Neighbor (KNN) gives an accuracy of 89,29%.

Predicting protein inter-residue contacts using composite likelihood maximization and deep learning

BackgroundAccurate prediction of inter-residue contacts of a protein is important to calculating its tertiary structure. Analysis of co-evolutionary events among residues has been proved effective in inferring inter-residue contacts. The Markov random field (MRF) technique, although being widely used for contact prediction, suffers from the following dilemma: the actual likelihood function of MRF is accurate but time-consuming to calculate; in contrast, approximations to the actual likelihood, say pseudo-likelihood, are efficient to calculate but inaccurate. Thus, how to achieve both accuracy and efficiency simultaneously remains a challenge.ResultsIn this study, we present such an approach (called clmDCA) for contact prediction. Unlike plmDCA using pseudo-likelihood, i.e., the product of conditional probability of individual residues, our approach uses composite-likelihood, i.e., the product of conditional probability of all residue pairs. Composite likelihood has been theoretically proved as a better approximation to the actual likelihood function than pseudo-likelihood. Meanwhile, composite likelihood is still efficient to maximize, thus ensuring the efficiency of clmDCA. We present comprehensive experiments on popular benchmark datasets, including PSICOV dataset and CASP-11 dataset, to show that: i) clmDCA alone outperforms the existing MRF-based approaches in prediction accuracy. ii) When equipped with deep learning technique for refinement, the prediction accuracy of clmDCA was further significantly improved, suggesting the suitability of clmDCA for subsequent refinement procedure. We further present a successful application of the predicted contacts to accurately build tertiary structures for proteins in the PSICOV dataset.ConclusionsComposite likelihood maximization algorithm can efficiently estimate the parameters of Markov Random Fields and can improve the prediction accuracy of protein inter-residue contacts.

Cooperative Co-Evolution Algorithm with an MRF-Based Decomposition Strategy for Stochastic Flexible Job Shop Scheduling

Flexible job shop scheduling is an important issue in the integration of research area and real-world applications. The traditional flexible scheduling problem always assumes that the processing time of each operation is fixed value and given in advance. However, the stochastic factors in the real-world applications cannot be ignored, especially for the processing times. We proposed a hybrid cooperative co-evolution algorithm with a Markov random field (MRF)-based decomposition strategy (hCEA-MRF) for solving the stochastic flexible scheduling problem with the objective to minimize the expectation and variance of makespan. First, an improved cooperative co-evolution algorithm which is good at preserving of evolutionary information is adopted in hCEA-MRF. Second, a MRF-based decomposition strategy is designed for decomposing all decision variables based on the learned network structure and the parameters of MRF. Then, a self-adaptive parameter strategy is adopted to overcome the status where the parameters cannot be accurately estimated when facing the stochastic factors. Finally, numerical experiments demonstrate the effectiveness and efficiency of the proposed algorithm and show the superiority compared with the state-of-the-art from the literature.

One-step adaptive markov random field for structured compressive sensing

Recently, Markov random fields (MRFs) have gained much success in sparse signal recovery. One of the challenges is to adaptively estimate the MRF parameters from a few compressed measurements in compressive sensing (CS). To address this problem, a recently developed method proposes to estimate the MRF parameters based on the point estimation of sparse signals. However, the point estimation cannot depict the statistical uncertainty of the latent sparse signal, which can result in inaccurate parameters estimation; thus, limiting the ultimate performance. In this study, we propose a one-step MRF based CS that estimates the MRF parameters from the given measurements through solving a maximum marginal likelihood (MML) problem. Since the marginal likelihood is obtained from averaging over the latent sparse signal population, it offers better generalization over all the latent sparse signals than the point estimation. To solve the MML problem effectively, we approximate the MRF distribution by the product of two simpler distributions, which enables to produce closed-form solutions for all unknown variables with low computational cost. Extensive experiments on a synthetic and three real-world datasets demonstrate the effectiveness of the proposed method in recovery accuracy, noise tolerance, and runtime.

MRF model-based joint interrupted SAR imaging and coherent change detection via variational Bayesian inference

Abstract In this paper, we study the problem of interrupted synthetic aperture radar (SAR) imaging and coherent change detection (CCD) in the setting of gapped collections with missing pulses. Conventional interrupted SAR CCD technique is performed using a coherence estimator for paired SAR images which are reconstructed by matched-filtering (MF). However, this method suffers from substantial false alarms due to the poor resolution and high sidelobe level problems in the reconstruction. To improve image resolution and lessen the number of false alarms, sparsity-driven (SD) estimation techniques have been utilized to form SAR image pair and then apply coherence estimator to the resulting images. Actually, existing SD-based regularization SAR imaging algorithms are sensitive to the regularized parameters which are required to tune manually, leading to a serious restriction in practical application. To solve this problem, in this work, we develop an adaptive joint imaging and CCD algorithm in interrupted environments based on Bayesian framework. Our formulation utilizes a partially coherent model to incorporate prior information about the scenes and properties of changes. In particular, we model the sparsity and spatial clustering in changes by virtue of a Markov random fields (MRF) prior. To tackle the difficulty of the calculation of posterior, the mean-field variational Bayesian expectation-maximization (VBEM) method is utilized to simultaneously estimate the MRF parameters and the latent variables. Experimental results are provided to verify the effectiveness of the proposed method.

Real-Time and Low-Power Streaming Source Separation Using Markov Random Field

Machine learning (ML) has revolutionized a wide range of recognition tasks, ranging from text analysis to speech to vision, most notably in cloud deployments. However, mobile deployment of these ideas involves a very different category of design problems. In this article, we develop a hardware architecture for a sound source separation task, intended for deployment on a mobile phone. We focus on a novel Markov random field (MRF) sound source separation algorithm that uses expectation-maximization and Gibbs sampling to learn MRF parameters on the fly and infer the best separation of sources. The intrinsically iterative algorithm suggests challenges for both speed and power. A real-time streaming FPGA implementation runs at 150MHz with 207KB RAM, achieves a speed-up of 22× over a software reference, performs with an SDR of up to 7.021dB with 1.601ms latency, and exhibits excellent perceived audio quality. A 45nm CMOS ASIC virtual prototype simulated at 20MHz shows that this architecture is small (<10 million gates) and consumes only 70mW, which is less than 2% of the power of an ARM Cortex-A9 software version. To the best of our knowledge, this is the first Gibbs sampling inference accelerator designed in conventional FPGA/ASIC technology that targets a realistic mobile perceptual application.

A regularized pan-sharpening approach based on self-similarity and Gabor prior

ABSTRACTIn this article, we propose a new regularization-based approach for pan-sharpening based on the concepts of self-similarity and Gabor prior. The given low spatial resolution (LR) and high spectral resolution multi-spectral (MS) image is modelled as degraded and noisy version of the unknown high spatial resolution (HR) version. Since this problem is ill-posed, we use regularization to obtain the final solution. In the proposed method, we first obtain an initial HR approximation of the unknown pan-sharpened image using self-similarity and sparse representation (SR) theory. Using self-similarity, we obtain the HR patches from the given LR observation by searching for matching patches in its coarser resolution, thereby obtaining LR–HR pairs. An SR framework is used to obtain the patch pairs for which no matches are available for the patches in LR observation. The entire set of matched HR patches constitutes initial HR approximation (initial estimate) to the final pan-sharpened image which is used to estimate the degradation matrix as used in our model. A regularization framework is then used to obtain the final solution in which we propose to use a new prior which we refer as Gabor prior that extracts the bandpass details from the registered panchromatic (Pan) image. In addition, we also include Markov random field (MRF) smoothness prior that preserves the smoothness in the final pan-sharpened image. MRF parameter is derived using the initial estimate image. The final cost function consists of data fitting term and two prior terms corresponding to Gabor and MRF. Since the derived cost function is convex, simple gradient-based method is used to obtain the final solution. The efficacy of the proposed method is evaluated by conducting the experiments on degraded as well as on un-degraded datasets of three different satellites, i.e., Ikonos-2, Quickbird, and Worldview-2. The results are compared on the basis of traditional measures as well as recently proposed quality with no reference (QNR) measure, which does not require the reference image.

An Edge Preserving Multiresolution Fusion: Use of Contourlet Transform and MRF Prior

In this paper, we propose a new approach for multiresolution fusion using contourlet transform (CT). The method is based on modeling the low spatial resolution (LR) and high spectral resolution multispectral (MS) image as the degraded and noisy version of their high spatial resolution version. Since this is an ill-posed problem, it requires regularization in order to obtain the final solution. In this paper, we first obtain the initial estimate of the fused image from the available MS image and the panchromatic (Pan) image by using the CT domain learning. Since CT provides better directional edges, the initial estimate has better edge details. Using the initial estimate, we obtain the degradation that accounts for the aliasing between the LR MS image and fused image. Regularization is carried out by modeling the texture of the final fused image as a homogeneous Markov random field (MRF) prior, where the MRF parameter is estimated using the initial estimate. The use of MRF prior on the final fused image takes care of the spatial dependencies among the pixels. A simple gradient-based optimization technique is used to obtain the final fused image. Although we use homogeneous MRF, the proposed approach preserves the edges in the final fused image by retaining the edges from the initial estimate and by carrying out the optimization on nonedge pixels only. Therefore, the advantage of the proposed method lies in preserving the discontinuities without using the discontinuity preserving prior, thus avoiding the use of computationally taxing optimization techniques for regularization purposes. In addition, the proposed method causes minimum spectral distortion since it learns the texture using contourlet coefficients and does not use actual Pan image pixel intensities. We demonstrate the effectiveness of our approach by conducting the experiments using subsampled and nonsubsampled CT on different data sets captured using Ikonos-2, Quickbird, and Worldview-2 satellites.

SU‐E‐J‐130: Automating Liver Segmentation Via Combined Global and Local Optimization

Purpose:The aim of this work is to develop a robust algorithm for accurate segmentation of liver with special attention paid to the problems with fuzzy edges and tumor.Methods:200 CT images were collected from radiotherapy treatment planning system. 150 datasets are selected as the panel data for shape dictionary and parameters estimation. The remaining 50 datasets were used as test images. In our study liver segmentation was formulated as optimization process of implicit function. The liver region was optimized via local and global optimization during iterations. Our method consists five steps: 1)The livers from the panel data were segmented manually by physicians, and then We estimated the parameters of GMM (Gaussian mixture model) and MRF (Markov random field). Shape dictionary was built by utilizing the 3D liver shapes. 2)The outlines of chest and abdomen were located according to rib structure in the input images, and the liver region was initialized based on GMM. 3)The liver shape for each 2D slice was adjusted using MRF within the neighborhood of liver edge for local optimization. 4)The 3D liver shape was corrected by employing SSR (sparse shape representation) based on liver shape dictionary for global optimization. Furthermore, H‐PSO(Hybrid Particle Swarm Optimization) was employed to solve the SSR equation. 5)The corrected 3D liver was divided into 2D slices as input data of the third step. The iteration was repeated within the local optimization and global optimization until it satisfied the suspension conditions (maximum iterations and changing rate).Results:The experiments indicated that our method performed well even for the CT images with fuzzy edge and tumors. Comparing with physician delineated results, the segmentation accuracy with the 50 test datasets (VOE, volume overlap percentage) was on average 91%–95%.Conclusion:The proposed automatic segmentation method provides a sensible technique for segmentation of CT images.This work is supported by NIH/NIBIB (1R01‐EB016777), National Natural Science Foundation of China (No.61471226 and No.61201441), Research funding from Shandong Province (No.BS2012DX038 and No.J12LN23), and Research funding from Jinan City (No.201401221 and No.20120109).

Computing the Cramer–Rao Bound of Markov Random Field Parameters: Application to the Ising and the Potts Models

This letter considers the problem of computing the Cramer-Rao bound for the parameters of a Markov random field. Computation of the exact bound is not feasible for most fields of interest because their likelihoods are intractable and have intractable derivatives. We show here how it is possible to formulate the computation of the bound as a statistical inference problem that can be solve approximately, but with arbitrarily high accuracy, by using a Monte Carlo method. The proposed methodology is successfully applied on the Ising and the Potts models.

A Joint Land Cover Mapping and Image Registration Algorithm Based on a Markov Random Field Model

Traditionally, image registration of multi-modal and multi-temporal images is performed satisfactorily before land cover mapping. However, since multi-modal and multi-temporal images are likely to be obtained from different satellite platforms and/or acquired at different times, perfect alignment is very difficult to achieve. As a result, a proper land cover mapping algorithm must be able to correct registration errors as well as perform an accurate classification. In this paper, we propose a joint classification and registration technique based on a Markov random field (MRF) model to simultaneously align two or more images and obtain a land cover map (LCM) of the scene. The expectation maximization (EM) algorithm is employed to solve the joint image classification and registration problem by iteratively estimating the map parameters and approximate posterior probabilities. Then, the maximum a posteriori (MAP) criterion is used to produce an optimum land cover map. We conducted experiments on a set of four simulated images and one pair of remotely sensed images to investigate the effectiveness and robustness of the proposed algorithm. Our results show that, with proper selection of a critical MRF parameter, the resulting LCMs derived from an unregistered image pair can achieve an accuracy that is as high as when images are perfectly aligned. Furthermore, the registration error can be greatly reduced.

Optimizing Nondecomposable Loss Functions in Structured Prediction

We develop an algorithm for structured prediction with nondecomposable performance measures. The algorithm learns parameters of Markov Random Fields (MRFs) and can be applied to multivariate performance measures. Examples include performance measures such as Fβ score (natural language processing), intersection over union (object category segmentation), Precision/Recall at k (search engines), and ROC area (binary classifiers). We attack this optimization problem by approximating the loss function with a piecewise linear function. The loss augmented inference forms a Quadratic Program (QP), which we solve using LP relaxation. We apply this approach to two tasks: object class-specific segmentation and human action retrieval from videos. We show significant improvement over baseline approaches that either use simple loss functions or simple scoring functions on the PASCAL VOC and H3D Segmentation datasets, and a nursing home action recognition dataset.

Variational segmentation algorithms with label frequency constraints

We consider image and signal segmentation problems within the Markov random field (MRF) approach and try to take into account label frequency constraints. Incorporating these constraints into MRF leads to an NP-hard optimization problem. For solving this problem we present a two-step approximation scheme that allows one to use hard, interval and soft constraints on label frequencies. On the first step a factorized approximation of the joint distribution is made (only local terms are included) and then, on the second step, the labeling is found by conditional maximization of the factorized joint distribution. The latter task is reduced to an easy-to-solve transportation problem. Basing on the proposed two-step approximation scheme we derive the ELM algorithm for tuning MRF parameters. We show the efficiency of our approach on toy signals and on the task of automated segmentation of Google Maps.

Prostate Cancer Segmentation With Simultaneous Estimation of Markov Random Field Parameters and Class

Prostate cancer is one of the leading causes of death from cancer among men in the United States. Currently, high-resolution magnetic resonance imaging (MRI) has been shown to have higher accuracy than trans-rectal ultrasound (TRUS) when used to ascertain the presence of prostate cancer. As MRI can provide both morphological and functional images for a tissue of interest, some researchers are exploring the uses of multispectral MRI to guide prostate biopsies and radiation therapy. However, success with prostate cancer localization based on current imaging methods has been limited due to overlap in feature space of benign and malignant tissues using any one MRI method and the interobserver variability. In this paper, we present a new unsupervised segmentation method for prostate cancer detection, using fuzzy Markov random fields (fuzzy MRFs) for the segmentation of multispectral MR prostate images. Typically, both hard and fuzzy MRF models have two groups of parameters to be estimated: the MRF parameters and class parameters for each pixel in the image. To date, these two parameters have been treated separately, and estimated in an alternating fashion. In this paper, we develop a new method to estimate the parameters defining the Markovian distribution of the measured data, while performing the data clustering simultaneously. We perform computer simulations on synthetic test images and multispectral MR prostate datasets to demonstrate the efficacy and efficiency of the proposed method and also provide a comparison with some of the commonly used methods.

Agentification of Markov model-based segmentation: Application to magnetic resonance brain scans

Markov random field (MRF) models have been traditionally applied to the task of robust-to-noise image segmentation. Most approaches estimate MRF parameters on the whole image via a global expectation-maximization (EM) procedure. The resulting estimated parameters are likely to be uncharacteristic of local image features. Instead, we propose to distribute a set of local MRF models within a multiagent framework. Local segmentation agents estimate local MRF models via local EM procedures and cooperate to ensure a global consistency of local models. We demonstrate different types of cooperations between agents that lead to additional levels of regularization compared to the standard label regularization provided by MRF. Embedding Markovian EM procedures into a multiagent paradigm shows interesting properties that are illustrated on magnetic resonance (MR) brain scan segmentation. A cooperative tissue and subcortical structure segmentation approach is designed with such a framework, where both models mutually improve. Several experiments are reported and illustrate the working of Markovian EM agents. The evaluation of MR brain scan segmentation was performed using both phantoms and real 3T brain scans. It showed a robustness to intensity non-uniformity and noise, together with a low computational time. Based on these experiments MRF agent-based approach appears to be a very promising new tool for complex image segmentation.

Markov Random Field Detection on Two-Dimensional Intersymbol Interference Channels

We present a novel iterative algorithm for detection of binary Markov random fields (MRFs) corrupted by 2-D intersymbol interference (ISI) and additive white Gaussian noise. We assume a first-order binary MRF as a simple model for correlated images. We assume a 2-D digital storage channel, where the MRF is interleaved before being written and then read by a 2-D transducer; such channels occur in recently proposed optical disk storage systems. The detection algorithm is a concatenation of two soft-input/soft-output (SISO) detectors: an iterative row-column soft-decision feedback (IRCSDF) ISI detector, and a MRF detector. The MRF detector is a SISO version of the stochastic relaxation algorithm by Geman and Geman. On the 2times2 averaging-mask ISI channel, at a bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> , the concatenated algorithm achieves SNR savings of between 0.2 and 2.0 dB over the IRCSDF detector alone; the savings increase as the MRFs become more correlated, or as the SNR decreases. The algorithm is also fairly robust to mismatches between the assumed and actual MRF parameters.

Scattering From Very Large Randomly Rough Surfaces Using a Markov Random Field Equivalent Current

A Markov random field (MRF) model is employed to learn the statistical properties of an equivalent current situated above a rough surface, where this equivalent current represents near-field electromagnetic scattered fields. The MRF parameters are learned by considering numerical scattering from a relatively small rough surface, which can be solved efficiently via existing numerical methods. The MRF parameters may then be used to synthesize multiple realizations of the equivalent current associated with scattering from a much larger rough surface. These equivalent currents may be used to efficiently calculate the far-field scattered-field statistics for large surfaces. The advantages of this approach are manifested in the fact that once the MRF parameters are learned, a forward model is no longer needed to generate random realizations of the equivalent currents, and the MRF model can be employed to generate equivalent surfaces of size beyond the capability of existing numerical models. To improve the accuracy of the MRF model, a narrowband filter is used to preprocess the computed current distributions prior to MRF model training. One-dimensional rough surfaces are considered here to demonstrate the idea, and the method of ordered multiple interactions (MOMI) is employed to perform the numerical forward modeling. Promising MRF-generated results are demonstrated, with comparison to direct MOMI solutions.

Iterative Source-Channel Decoding With Markov Random Field Source Models

We propose a joint source-channel decoding approach for multidimensional correlated source signals. A Markov random field (MRF) source model is used which exemplarily considers the residual spatial correlations in an image signal after source encoding. Furthermore, the MRF parameters are selected via an analysis based on extrinsic information transfer charts. Due to the link between MRFs and the Gibbs distribution, the resulting soft-input soft-output (SISO) source decoder can be implemented with very low complexity. We prove that the inclusion of a high-rate block code after the quantization stage allows the MRF-based decoder to yield the maximum average extrinsic information. When channel codes are used for additional error protection the MRF-based SISO source decoder can be used as the outer constituent decoder in an iterative source-channel decoding scheme. Considering an example of a simple image transmission system we show that iterative decoding can be successfully employed for recovering the image data, especially when the channel is heavily corrupted

Detection of microcalcifications in digital mammograms using wavelet filter and Markov random field model

Clustered microcalcifcations (MCs) in digitized mammograms has been widely recognized as an early sign of breast cancer in women. This work is devoted to developing a computer-aided diagnosis (CAD) system for the detection of MCs in digital mammograms. Such a task actually involves two key issues: detection of suspicious MCs and recognition of true MCs. Accordingly, our approach is divided into two stages. At first, all suspicious MCs are preserved by thresholding a filtered mammogram via a wavelet filter according to the MPV (mean pixel value) of that image. Subsequently, Markov random field parameters based on the Derin–Elliott model are extracted from the neighborhood of every suspicious MCs as the primary texture features. The primary features combined with three auxiliary texture quantities serve as inputs to classifiers for the recognition of true MCs so as to decrease the false positive rate. Both Bayes classifier and back-propagation neural network were used for computer experiments. The data used to test this method were 20 mammograms containing 25 areas of clustered MCs marked by radiologists. Our method can readily remove 1341 false positives out of 1356, namely, 98.9% false positives were removed. Additionally, the sensitivity (true positives rate) is 92%, with only 0.75 false positives per image. From our experiments, we conclude that, with a proper choice of classifier, the texture feature based on Markov random field parameters combined with properly designed auxiliary features extracted from the texture context of the MCs can work outstandingly in the recognition of MCs in digital mammograms.