Prestack inversion based on anisotropic Markov random field-maximum posterior probability inversion and its application to identify shale gas sweet spots

Economic shale gas production requires hydraulic fracture stimulation to increase the formation permeability. Hydraulic fracturing strongly depends on geomechanical parameters such as Young＇s modulus and Poisson＇s ratio. Fracture-prone sweet spots can be predicted by prestack inversion, which is an ill-posed problem; thus, regularization is needed to obtain unique and stable solutions. To characterize gas-bearing shale sedimentary bodies, elastic parameter variations are regarded as an anisotropic Markov random field. Bayesian statistics are adopted for transforming prestack inversion to the maximum posterior probability. Two energy functions for the lateral and vertical directions are used to describe the distribution, and the expectation-maximization algorithm is used to estimate the hyperparameters of the prior probability of elastic parameters. Finally, the inversion yields clear geological boundaries, high vertical resolution, and reasonable lateral continuity using the conjugate gradient method to minimize the objective function. Antinoise and imaging ability of the method were tested using synthetic and real data.

Fast segmentation approach for SAR image based on simple Markov random field

Traditional image segmentation methods based on MRF converge slowly and require pre-defined weight. These disadvantages are addressed, and a fast segmentation approach based on simple Markov random field （MRF） for SAR image is proposed. The approach is firstly used to perform coarse segmentation in blocks. Then the image is modeled with simple MRF and adaptive variable weighting forms are applied in homogeneous and heterogeneous regions. As a result, the convergent speed is accelerated while the segmentation results in homogeneous regions and boarders are improved. Simulations with synthetic and real SAR images demonstrate the effectiveness of the proposed approach.

Optimization by Estimation of Distribution with DEUM Framework Based on Markov Random Fields

This paper presents a Markov random field （MRP） approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields （DEUM）. DEUM is a subclass of estimation of distribution algorithms （EDAs） where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are： 1） use of MRF models, 2） fitness modeling approach to estimating the parameter of the model and 3） Monte Carlo approach to sampling from the model.

STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE

This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.

Image Dehazing by Incorporating Markov Random Field with Dark Channel Prior

As one of the most simple and effective single image dehazing methods, the dark channel prior(DCP) algorithm has been widely applied. However, the algorithm does not work for pixels similar to airlight(e.g., snowy ground or a white wall), resulting in underestimation of the transmittance of some local scenes. To address that problem, we propose an image dehazing method by incorporating Markov random field(MRF) with the DCP. The DCP explicitly represents the input image observation in the MRF model obtained by the transmittance map. The key idea is that the sparsely distributed wrongly estimated transmittance can be corrected by properly characterizing the spatial dependencies between the neighboring pixels of the transmittances that are well estimated and those that are wrongly estimated. To that purpose, the energy function of the MRF model is designed. The estimation of the initial transmittance map is pixel-based using the DCP, and the segmentation on the transmittance map is employed to separate the foreground and background, thereby avoiding the block effect and artifacts at the depth discontinuity. Given the limited number of labels obtained by clustering, the smoothing term in the MRF model can properly smooth the transmittance map without an extra refinement filter. Experimental results obtained by using terrestrial and underwater images are given.

基于Markov随机场模型的数字X光图像自适应增强算法

为明确X光图像纹理粗细和组织分布状况,强化呈现身体结构信息,降低模糊图像对医生诊断病情结果的错误判断,提出一种基于Markov随机场模型的数字X光图像自适应增强算法.该算法首先统计X光图像全部范围内相同亮度像素,利用直方图均衡化法将原始图像变换成灰度级分布影像,消除光线干扰;然后分析组织属性,通过灰度共生矩阵提取X光图像的纹理特征,获取图像纹理粗细和布局结构的灰度信息;最后通过映射函数和对数函数计算平均亮度,用Markov随机场模型调整图像明暗度,补充纹理细小部位亮度,再用随机场函数划分光滑图像,采取二次重构,以保证图像锐化增强效果平衡.仿真实验结果表明,该算法能提升图像的内部信息清晰度.

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,

Reservoir lithology stochastic simulation based on Markov random fields

Markov random fields(MRF) have potential for predicting and simulating petroleum reservoir facies more accurately from sample data such as logging, core data and seismic data because they can incorporate interclass relationships. While, many relative studies were based on Markov chain, not MRF, and using Markov chain model for 3D reservoir stochastic simulation has always been the difficulty in reservoir stochastic simulation. MRF was proposed to simulate type variables(for example lithofacies) in this work. Firstly, a Gibbs distribution was proposed to characterize reservoir heterogeneity for building 3-D(three-dimensional) MRF. Secondly, maximum likelihood approaches of model parameters on well data and training image were considered. Compared with the simulation results of MC(Markov chain), the MRF can better reflect the spatial distribution characteristics of sand body.

A User Participation Behavior Prediction Model of Social Hotspots Based on Influence and Markov Random Field

Hotspot topic trends can be captured by analyzing user attributes and historical behavior in social network. In this paper, we propose a user participation behavior prediction model for social hotspots, based on user behavior and relationship data, to predict user participation behavior and topic development trends. Firstly, for the complex factors of user behavior, three dynamic influence factor functions are defined, including individual, peer and community influence. These functions take timeliness into account using a time discretization method. Secondly, to determine laws of individual behavior and group behavior within a social topic, a hotspot user participation behavior prediction model is proposed and associated with the basic concepts of randora field and Markov property in information diffusion. The experimental results show that the model can not only dynamically predict the individual behavior, but also grasp the development trends of topics.

Coherence-coefficient-based Markov random field approach for building segmentation from high-resolution SAR images

Building segmentation from high-resolution synthetic aperture radar (SAR) images has always been one of the important research issues. Due to the existence of speckle noise and multipath effect, the pixel values change drastically, causing the large intensity differences in pixels of building areas. Moreover, the geometric structure of buildings can cause strong scattering spots, which brings difficulties to the segmentation and extraction of buildings. To solve of these problems, this paper presents a coherence-coefficient-based Markov random field (CCMRF) approach for building segmentation from high-resolution SAR images. The method introduces the coherence coefficient of interferometric synthetic aperture radar (InSAR) into the neighborhood energy based on traditional Markov random field (MRF), which makes interferometric and spatial contextual information more fully used in SAR image segmentation. According to the Hammersley-Clifford theorem, the problem of maximum a posteriori (MAP) for image segmentation is transformed into the solution of minimizing the sum of likelihood energy and neighborhood energy. Finally, the iterative condition model (ICM) is used to find the optimal solution. The experimental results demonstrate that the proposed method can segment SAR building effectively and obtain more accurate results than the traditional MRF method and K-means clustering.

A New Encryption-Then-Compression Scheme on Gray Images Using the Markov Random Field

Compressing encrypted images remains a challenge.As illustrated in our previous work on compression of encrypted binary images,it is preferable to exploit statistical characteristics at the receiver.Through this line,we characterize statistical correlations between adjacent bitplanes of a gray image with the Markov random field(MRF),represent it with a factor graph,and integrate the constructed MRF factor graph in that for binary image reconstruction,which gives rise to a joint factor graph for gray images reconstruction(JFGIR).By exploiting the JFGIR at the receiver to facilitate the reconstruction of the original bitplanes and deriving theoretically the sum-product algorithm(SPA)adapted to the JFGIR,a novel MRF-based encryption-then-compression(ETC)scheme is thus proposed.After preferable universal parameters of the MRF between adjacent bitplanes are sought via a numerical manner,extensive experimental simulations are then carried out to show that the proposed scheme successfully compresses the first 3 and 4 most significant bitplanes(MSBs)for most test gray images and the others with a large portion of smooth area,respectively.Thus,the proposed scheme achieves significant improvement against the state-of-the-art leveraging the 2-D Markov source model at the receiver and is comparable or somewhat inferior to that using the resolution-progressive strategy in recovery.

An Improved Non-Parametric Method for Multiple Moving Objects Detection in the Markov Random Field

Detecting moving objects in the stationary background is an important problem in visual surveillance systems.However,the traditional background subtraction method fails when the background is not completely stationary and involves certain dynamic changes.In this paper,according to the basic steps of the background subtraction method,a novel non-parametric moving object detection method is proposed based on an improved ant colony algorithm by using the Markov random field.Concretely,the contributions are as follows:1)A new nonparametric strategy is utilized to model the background,based on an improved kernel density estimation;this approach uses an adaptive bandwidth,and the fused features combine the colours,gradients and positions.2)A Markov random field method based on this adaptive background model via the constraint of the spatial context is proposed to extract objects.3)The posterior function is maximized efficiently by using an improved ant colony system algorithm.Extensive experiments show that the proposed method demonstrates a better performance than many existing state-of-the-art methods.

Magnetic-resonance image segmentation based on improved variable weight multi-resolution Markov random field in undecimated complex wavelet domain

To solve the problem that the magnetic resonance(MR)image has weak boundaries,large amount of information,and low signal-to-noise ratio,we propose an image segmentation method based on the multi-resolution Markov random field(MRMRF)model.The algorithm uses undecimated dual-tree complex wavelet transformation to transform the image into multiple scales.The transformed low-frequency scale histogram is used to improve the initial clustering center of the K-means algorithm,and then other cluster centers are selected according to the maximum distance rule to obtain the coarse-scale segmentation.The results are then segmented by the improved MRMRF model.In order to solve the problem of fuzzy edge segmentation caused by the gray level inhomogeneity of MR image segmentation under the MRMRF model,it is proposed to introduce variable weight parameters in the segmentation process of each scale.Furthermore,the final segmentation results are optimized.We name this algorithm the variable-weight multi-resolution Markov random field(VWMRMRF).The simulation and clinical MR image segmentation verification show that the VWMRMRF algorithm has high segmentation accuracy and robustness,and can accurately and stably achieve low signal-to-noise ratio,weak boundary MR image segmentation.

CLOUD IMAGE DETECTION BASED ON MARKOV RANDOM FIELD

In order to overcome the disadvantages of low accuracy rate, high complexity and poor robustness to image noise in many traditional algorithms of cloud image detection, this paper proposed a novel algorithm on the basis of Markov Random Field (MRF) modeling. This paper first defined algorithm model and derived the core factors affecting the performance of the algorithm, and then, the solving of this algorithm was obtained by the use of Belief Propagation (BP) algorithm and Iterated Conditional Modes (ICM) algorithm. Finally, experiments indicate that this algorithm for the cloud image detection has higher average accuracy rate which is about 98.76% and the average result can also reach 96.92% for different type of image noise.

Fusing PLSA model and Markov random fields for automatic image annotation

A novel image auto-annotation method is presented based on probabilistic latent semantic analysis(PLSA) model and multiple Markov random fields(MRF).A PLSA model with asymmetric modalities is first constructed to estimate the joint probability between images and semantic concepts,then a subgraph is extracted served as the corresponding structure of Markov random fields and inference over it is performed by the iterative conditional modes so as to capture the final annotation for the image.The novelty of our method mainly lies in two aspects:exploiting PLSA to estimate the joint probability between images and semantic concepts as well as multiple MRF to further explore the semantic context among keywords for accurate image annotation.To demonstrate the effectiveness of this approach,an experiment on the Corel5 k dataset is conducted and its results are compared favorably with the current state-of-the-art approaches.

Segmentation of MS lesions using entropy-based EM algorithm and Markov random fields

This paper presents an approach for fully automatic segmentation of MS lesions in fluid attenuated inversion recovery (FLAIR) Magnetic Resonance (MR) images. The proposed method estimates a gaussian mixture model with three kernels as cerebrospinal fluid (CSF), normal tissue and Multiple Sclerosis lesions. To estimate this model, an automatic Entropy based EM algorithm is used to find the best estimated Model. Then, Markov random field (MRF) model and EM algorithm are utilized to obtain and upgrade the class conditional probability density function and the apriori probability of each class. After estimation of Model parameters and apriori probability, brain tissues are classified using bayesian classification. To evaluate the result of the proposed method, similarity criteria of different slices related to 20 MS patients are calculated and compared with other methods which include manual segmentation. Also, volume of segmented lesions are computed and compared with gold standard using correlation coefficient. The proposed method has better performance in comparison with previous works which are reported here.

Elitist Reconstruction Genetic Algorithm Based on Markov Random Field for Magnetic Resonance Image Segmentation

In this paper, elitist reconstruction genetic algorithm （ERGA） based on Markov random field （MRF） is introduced for image segmentation. In this algorithm, a population of possible solutions is maintained at every generation, and for each solution a fitness value is calculated according to a fitness function, which is constructed based on the MRF potential function according to Metropolis function and Bayesian framework. After the improved selection, crossover and mutation, an elitist individual is restructured based on the strategy of restructuring elitist. This procedure is processed to select the location that denotes the largest MRF potential function value in the same location of all individuals. The algorithm is stopped when the change of fitness functions between two sequent generations is less than a specified value. Experiments show that the performance of the hybrid algorithm is better than that of some traditional algorithms.

Some Strong Limit Theorems for Even-odd Markov Chain Fields Indexed by Trees

First,a class of strong limit theorems are proved by constructing two nonnegative martingales.Then they are applied to the study of all kinds of even-odd Markov chain fields and Markov chain fields defined in the paper.Finally,some strong limit theorems for the even-odd Markov chain fields and Markov chain fields are obtained.

THE DECISION OF THE OPTIMAL PARAMETERS IN MARKOV RANDOM FIELDS OF IMAGES BY GENETIC ALGORITHM

This paper introduces the principle of genetic algorithm and the basic method of solving Markov random field parameters.Focusing on the shortcomings in present methods,a new method based on genetic algorithms is proposed to solve the parameters in the Markov random field.The detailed procedure is discussed.On the basis of the parameters solved by genetic algorithms,some experiments on classification of aerial images are given.Experimental results show that the proposed method is effective and the classification results are satisfactory.

ON MARKOV RANDOM FIELD MODELS FOR SEGMENTATION OF NOISY IMAGES

Markov random field(MRF) models for segmentation of noisy images are discussed. According to the maximum a posteriori criterion, a configuration of an image field is regarded as an optimal estimate of the original scene when its energy is minimized. However, the minimum energy configuration does not correspond to the scene on edges of a given image, which results in errors of segmentation. Improvements of the model are made and a relaxation algorithm based on the improved model is presented using the edge information obtained by a coarse-to-fine procedure. Some examples are presented to illustrate the applicability of the algorithm to segmentation of noisy images.