一种基于马尔可夫随机场的SAR图像分割新方法

该文提出了一种基于马尔可夫随机场(MRF)的合成孔径雷达(SAR)图像分割新方法。在传统MRF的邻域基团势函数基础上,引入了图像邻域中各个像素的强度差值以及像素之间的距离因子,使SAR图像中空间上下文信息得到了更加充分的利用。根据贝叶斯定理将图像分割问题转化为最大后验概率的求取问题,运用迭代条件模型(ICM)算法求得最大后验概率的解。在实验中,将该文提出的方法、传统上使用ICM以及模拟退火(SA)优化方法的MRF分割运用于模拟的SAR图像以及真实SAR图像。比较结果证明,该文的方法在误分率以及抗噪性上更具优势。     

基于上下文和隐类属的小波域马尔可夫随机场SAR图像分割

该文针对合成孔径雷达(Synthetic Aperture Radar, SAR)图像含有大量的乘性斑点噪声的特点,提出了一种小波域隐类属的马尔可夫随机场(Markov Random Field, MRF)图像分割算法来抑制噪声的影响。考虑到小波的聚集性和持续性,该算法重新构造了待分图像小波域模型以类属为隐状态的混合长拖尾模型,将隐类属的马尔可夫随机场推广到小波域上,并用改进的上下文模型估计尺度间转移概率,最后推导出了新的最大后验(Maximum A Posteriori, MAP)分割公式。仿真结果证明,该算法具有鲁棒性能够有效地抑制噪声对图像的影响,得到准确的分割结果。     

A multiscale random field model for Bayesian image segmentation

Many approaches to Bayesian image segmentation have used maximum a posteriori (MAP) estimation in conjunction with Markov random fields (MRF). Although this approach performs well, it has a number of disadvantages. In particular, exact MAP estimates cannot be computed, approximate MAP estimates are computationally expensive to compute, and unsupervised parameter estimation of the MRF is difficult. The authors propose a new approach to Bayesian image segmentation that directly addresses these problems. The new method replaces the MRF model with a novel multiscale random field (MSRF) and replaces the MAP estimator with a sequential MAP (SMAP) estimator derived from a novel estimation criteria. Together, the proposed estimator and model result in a segmentation algorithm that is not iterative and can be computed in time proportional to MN where M is the number of classes and N is the number of pixels. The also develop a computationally efficient method for unsupervised estimation of model parameters. Simulations on synthetic images indicate that the new algorithm performs better and requires much less computation than MAP estimation using simulated annealing. The algorithm is also found to improve classification accuracy when applied to the segmentation of multispectral remotely sensed images with ground truth data.     

Statistical approach to segmentation of single-channel cerebral MRimages

A statistical model is presented that represents the distributions of major tissue classes in single-channel magnetic resonance (MR) cerebral images. Using the model, cerebral images are segmented into gray matter, white matter, and cerebrospinal fluid (CSF). The model accounts for random noise, magnetic field inhomogeneities, and biological variations of the tissues. Intensity measurements are modeled by a finite Gaussian mixture. Smoothness and piecewise contiguous nature of the tissue regions are modeled by a three-dimensional (3-D) Markov random field (MRF). A segmentation algorithm, based on the statistical model, approximately finds the maximum a posteriori (MAP) estimation of the segmentation and estimates the model parameters from the image data. The proposed scheme for segmentation is based on the iterative conditional modes (ICM) algorithm in which measurement model parameters are estimated using local information at each site, and the prior model parameters are estimated using the segmentation after each cycle of iterations. Application of the algorithm to a sample of clinical MR brain scans, comparisons of the algorithm with other statistical methods, and a validation study with a phantom are presented. The algorithm constitutes a significant step toward a complete data driven unsupervised approach to segmentation of MR images in the presence of the random noise and intensity inhomogeneities     

A unified framework for MAP estimation in remote sensing image segmentation

A complete framework is proposed for applying the maximum a posteriori (MAP) estimation principle in remote sensing image segmentation. The MAP principle provides an estimate for the segmented image by maximizing the posterior probabilities of the classes defined in the image. The posterior probability can be represented as the product of the class conditional probability (CCP) and the class prior probability (CPP). In this paper, novel supervised algorithms for the CCP and the CPP estimations are proposed which are appropriate for remote sensing images where the estimation process might to be done in high-dimensional spaces. For the CCP, a supervised algorithm which uses the support vector machines (SVM) density estimation approach is proposed. This algorithm uses a novel learning procedure, derived from the main field theory, which avoids the (hard) quadratic optimization problem arising from the traditional formulation of the SVM density estimation. For the CPP estimation, Markov random field (MRF) is a common choice which incorporates contextual and geometrical information in the estimation process. Instead of using predefined values for the parameters of the MRF, an analytical algorithm is proposed which automatically identifies the values of the MRF parameters. The proposed framework is built in an iterative setup which refines the estimated image to get the optimum solution. Experiments using both synthetic and real remote sensing data (multispectral and hyperspectral) show the powerful performance of the proposed framework. The results show that the proposed density estimation algorithm outperforms other algorithms for remote sensing data over a wide range of spectral dimensions. The MRF modeling raises the segmentation accuracy by up to 10% in remote sensing images.     

Posterior-mean super-resolution with a causal Gaussian Markov random field prior

We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with the line process supplies a preferable prior for natural images with edges. We improve the existing image transformation model, the compound MRF model, and its hyperparameter prior model. We also derive the optimal estimator--not the joint maximum a posteriori (MAP) or the marginalized maximum likelihood (ML) but the posterior mean (PM)--from the objective function of the L2-norm-based (mean square error) peak signal-to-noise ratio. Point estimates such as MAP and ML are generally not stable in ill-posed high-dimensional problems because of overfitting, whereas PM is a stable estimator because all the parameters in the model are evaluated as distributions. The estimator is numerically determined by using the variational Bayesian method. The variational Bayesian method is a widely used method that approximately determines a complicated posterior distribution, but it is generally hard to use because it needs the conjugate prior. We solve this problem with simple Taylor approximations. Experimental results have shown that the proposed method is more accurate or comparable to existing methods.     

一种采用高斯隐马尔可夫随机场模型的遥感图像分类算法

该文研究了无监督遥感图像分类问题。文中构造了图像的隐马尔可夫随机场模型(HiddenMarkov Random Fleid,HMRF),并且提出了基于该模型的图像分类算法。该文采用有限高斯混合模型(Finite Gaussian Mixture,FGM)描述图像像素灰度的条件概率分布,使用EM(Expectation-Maximization)算法解决从不完整数据中估计概率模型参数问题。针对遥感图像分布的不均匀特性,该文提出的算法没有采用固定的马尔可夫随机场模型参数,而是在递归分类算法中分级地调整模型参数以适应区域的变化。实验结果表明了该文算法的有效性,分类算法处理精度高于C-Means聚类算法.。     

Multiple abdominal organ segmentation: an atlas-based fuzzy connectedness approach.

Organ segmentation is an important step in various medical image applications. In this paper, a presegmented atlas is incorporated into the fuzzy connectedness (FC) framework for automatic segmentation of abdominal organs. First, the atlas is registered onto the subject to provide an initial segmentation. Then, a novel method is applied to estimate the necessary FC parameters such as organ intensity features, seeds, and optimal FC threshold automatically and subject adaptively. In order to overcome the intensity overlapping between the neighboring organs, a shape modification approach based on Euclidean distance and watershed segmentation is used. This atlas-based segmentation method has been tested on some abdominal CT and MRI images from Chinese patients. Experimental results indicate the validity of this segmentation method for various image modalities.     

A tree-structured Markov random field model for Bayesian image segmentation

We present a new image segmentation algorithm based on a tree-structured binary MRF model. The image is recursively segmented in smaller and smaller regions until a stopping condition, local to each region, is met. Each elementary binary segmentation is obtained as the solution of a MAP estimation problem, with the region prior modeled as an MRF. Since only binary fields are used, and thanks to the tree structure, the algorithm is quite fast, and allows one to address the cluster validation problem in a seamless way. In addition, all field parameters are estimated locally, allowing for some spatial adaptivity. To improve segmentation accuracy, a split-and-merge procedure is also developed and a spatially adaptive MRF model is used. Numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on "flat" MRF models, and its performance, in terms of segmentation accuracy and map smoothness, is comparable or even superior.     

基于扩散方程和MRF的SAR图像分割

该文提出了一种基于图像扩散方程和马尔科夫随机场(MRF)的合成孔径雷达(SAR)图像分割方法。在传统MRF算法的基础之中,引入对图像的扩散,用来平滑SAR图像中的噪声,保护图像中的边缘部分,并且加快收敛的速度。首先对输入的SAR图像进行扩散,通过MRF进行统计,得到图像中各点的后验概率,再对得到的后验概率进行扩散。与传统的MRF算法进行比较,该文的方法较好地去除了误分割斑块,减少算法的运行时间。     

Unsupervised segmentation of synthetic aperture Radar sea ice imagery using a novel Markov random field model

Environmental and sensor challenges pose difficulties for the development of computer-assisted algorithms to segment synthetic aperture radar (SAR) sea ice imagery. In this research, in support of operational activities at the Canadian Ice Service, images containing visually separable classes of either ice and water or multiple ice classes are segmented. This work uses image intensity to discriminate ice from water and uses texture features to identify distinct ice types. In order to seamlessly combine image spatial relationships with various image features, a novel Bayesian segmentation approach is developed and applied. This new approach uses a function-based parameter to weight the two components in a Markov random field (MRF) model. The devised model allows for automatic estimation of MRF model parameters to produce accurate unsupervised segmentation results. Experiments demonstrate that the proposed algorithm is able to successfully segment various SAR sea ice images and achieve improvement over existing published methods including the standard MRF-based method, finite Gamma mixture model, and K-means clustering.     

Unsupervised vector image segmentation by a tree structure-ICM algorithm

In recent years, many image segmentation approaches have been based on Markov random fields (MRFs). The main assumption of the MRF approaches is that the class parameters are known or can be obtained from training data. In this paper the authors propose a novel method that relaxes this assumption and allows for simultaneous parameter estimation and vector image segmentation. The method is based on a tree structure (TS) algorithm which is combined with Besag's iterated conditional modes (ICM) procedure. The TS algorithm provides a mechanism for choosing initial cluster centers needed for initialization of the ICM. The authors' method has been tested on various one-dimensional (1-D) and multidimensional medical images and shows excellent performance. In this paper the authors also address the problem of cluster validation. They propose a new maximum a posteriori (MAP) criterion for determination of the number of classes and compare its performance to other approaches by computer simulations.     

Adaptive segmentation of textured images by using the coupled Markov random field model.

Although simple and efficient, traditional feature-based texture segmentation methods usually suffer from the intrinsical less inaccuracy, which is mainly caused by the oversimplified assumption that each textured subimage used to estimate a feature is homogeneous. To solve this problem, an adaptive segmentation algorithm based on the coupled Markov random field (CMRF) model is proposed in this paper. The CMRF model has two mutually dependent components: one models the observed image to estimate features, and the other models the labeling to achieve segmentation. When calculating the feature of each pixel, the homogeneity of the subimage is ensured by using only the pixels currently labeled as the same pattern. With the acquired features, the labeling is obtained through solving a maximum a posteriori problem. In our adaptive approach, the feature set and the labeling are mutually dependent on each other, and therefore are alternately optimized by using a simulated annealing scheme. With the gradual improvement of features' accuracy, the labeling is able to locate the exact boundary of each texture pattern adaptively. The proposed algorithm is compared with a simple MRF model based method in segmentation of Brodatz texture mosaics and real scene images. The satisfying experimental results demonstrate that the proposed approach can differentiate textured images more accurately.     

A segmentation model using compound Markov random fields based on a boundary model.

Markov random field (MRF) theory has been widely applied to the challenging problem of image segmentation. In this paper, we propose a new nontexture segmentation model using compound MRFs, in which the original label MRF is coupled with a new boundary MRF to help improve the segmentation performance. The boundary model is relatively general and does not need prior training on boundary patterns. Unlike some existing related work, the proposed method offers a more compact interaction between label and boundary MRFs. Furthermore, our boundary model systematically takes into account all the possible scenarios of a single edge existing in a 3 x 3 neighborhood and, thus, incorporates sophisticated prior information about the relation between label and boundary. It is experimentally shown that the proposed model can segment objects with complex boundaries and at the same time is able to work under noise corruption. The new method has been applied to medical image segmentation. Experiments on synthetic images and real clinical datasets show that the proposed model is able to produce more accurate segmentation results and satisfactorily keep the delicate boundary. It is also less sensitive to noise in both high and low signal-to-noise ratio regions than some of the existing models in common use.     

Unsupervised multi class segmentation of 3D images with intensity inhomogeneities

Intensity inhomogeneities in images cause problems in gray-value based image segmentation since the varying intensity often dominates over gray-value differences of the image structures. In this paper we propose a novel biconvex variational model that includes the intensity inhomogeneities to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. In our model we assume that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of the resulting biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images serving as a motivation for our work.     

基于不完全分层MRF的非监督图象分割

分层马尔可夫随机场(MRF)图象模型由于层间具有因果关系,且这种因果关系符合图象的性质,使基于该模型的图象处理时间比平面MRF模型所用的时间大为减少.针对作者提出的一种新的分层马尔可夫图象模型——不完全分层模型,导出EM算法以估计模型参数.算法继承了分层模型非迭代算法运算速度快的优点,并因为模型结构的简化进一步减少了计算量,算法在模型的最上层加入了平面节点间信息的交互,以较少的计算换来了更加精确的参数估计结果.算法用于图象非监督分割的实验表明,和分层模型算法相比,其处理速度更快、由所估计的参数得到了更好或相当的分割结果,尤其适合大幅面图象的处理.     

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.     

An image change detection algorithm based on Markov random field models

This paper addresses the problem of image change detection (ICD) based on Markov random field (MRF) models. MRF has long been recognized as an accurate model to describe a variety of image characteristics. Here, we use the MRF to model both noiseless images obtained from the actual scene and change images (CIs), the sites of which indicate changes between a pair of observed images. The optimum ICD algorithm under the maximum a posteriori (MAP) criterion is developed under this model. Examples are presented for illustration and performance evaluation.     

Pixon-based image segmentation with Markov random fields

Image segmentation is an essential processing step for many image analysis applications. We propose a novel pixon-based adaptive scale method for image segmentation. The key idea of our approach is that a pixon-based image model is combined with a Markov random field (MRF) model under a Bayesian framework. We introduce a new pixon scheme that is more suitable for image segmentation than the "fuzzy" pixon scheme. The anisotropic diffusion equation is successfully used to form the pixons in our new pixon scheme. Experimental results demonstrate that our algorithm performs fairly well and computational costs decrease dramatically compared with the pixel-based MRF algorithm.