Adaptive scale fixing for multiscale texture segmentation.

This paper addresses two challenging issues in unsupervised multiscale texture segmentation: determining adequate spatial and feature resolutions for different regions of the image, and utilizing information across different scales/resolutions. The center of a homogeneous texture is analyzed using coarse spatial resolution, and its border is detected using fine spatial resolution so as to locate the boundary accurately. The extraction of texture features is achieved via a multiresolution pyramid. The feature values are integrated across scales/resolutions adaptively. The number of textures is determined automatically using the variance ratio criterion. Experimental results on synthetic and real images demonstrate the improvement in performance of the proposed multiscale scheme over single scale approaches.     

基于小波变换和马尔可夫随机场的极化SAR图像自动分类

本文提出一种对极化合成孔径雷达(SAR)图像进行自动多分辨率分类的方法。首先利用多视极化白化滤波(MPWF)抑制极化SAR图像的相干斑,得到反映地物辐射特征的纹理SAR图像,然后利用小波变换(WT)提取不同分辨率的纹理信息,在最低分辨率级利用Akaik信息准则(AIC)自动估计图像中的纹理类数,进而在各个分辨率级利用马尔可夫随机场(MRF)模型表征各像素间的空间关联信息,并分别利用最大似然(ML)方法和循环条件模式(ICM)进行自动的模型参数估计和最大后验概率(MAP)分类,最后应用NASA/JPL机载L波段极化SAR数据验证了本文所提分类方法的有效性和优越性。     

Infrared Texture Simulation Using Gaussian-Markov Random Fields

Infrared battlefield simulation is a most important subject today to test infrared weapons. The reality and details of simulated scenes are always relied on the infrared textures. A texture is considered to be a stochastic, possibly periodic, two-dimensional image field. A texture model can be described as a mathematical procedure. Markov random field(MRF) model is a famous model to synthesize the visible textures of various kinds. In this paper, the Gaussian-Markov random fields(GMRF) are firstly used to sample the distribution of temperature field on the surface of terrain. And the Planck's radiation law is applied to calculate the emittance in the bands of 3～5 μ m or 8～14 μ m. The emittance distribution of the terrain can be normalized and colored by the range of 0 to the gray levels decreased by 1. Then an infrared texture is generated by GMRF by given a set of certain parameters.     

基于混合高斯模型的三马尔可夫场红外图像分割

针对马尔可夫随机场在红外图像分割方面存在的问题,给出了一种基于混合高斯模型的三马尔可夫场红外图像分割算法.三马尔可夫场在马尔可夫随机场的基础上通过引入一个附加随机场和全体随机变量服从马尔可夫性假设,克服了马尔可夫场算法中对条件概率分布相互独立的要求,并赋予该附加随机场对目标和背景区域的标识作用,其中采用混合高斯模型作为三马尔可夫随机场的先验模型.仿真结果表明,文中提出的基于混合高斯模型的三马尔可夫场红外图像分割算法能够实现复杂背景的红外图像准确分割,得到较为理想的分割效果.     

Multivariate Gaussian MRF for multispectral scene segmentation andanomaly detection

Gaussian Markov random field texture models and multivariate parametric clustering algorithms have been applied extensively for segmentation, restoration, and anomaly detection of single-band and multispectral imagery, respectively. The present work extends and combines these previous efforts to demonstrate joint spatial-spectral modeling of multispectral imagery, a multivariate (vector observations) GMRF texture model is employed. Algorithms for parameter estimation and image segmentation are discussed, and a new anomaly detection technique is developed. The model is applied to imagery from the Daedalus sensor. Image segmentation results from test images are discussed and compared to spectral clustering results. The test images are collages, with known texture boundaries constructed from larger data cubes. Anomaly detection results for two Daedalus images are also presented, assessed using receiver operating characteristic (ROC) performance curves, and compared to spectral clustering models. It is demonstrated that even the simplest first-order isotropic texture models provide significant improvement in image segmentation and anomaly detection over pure spectral clustering for the data sets examined. The sensitivity of anomaly detection performance to the choice of parameter estimation method and to the number of texture segments is examined for one example data set     

基于高斯-马尔可夫随机场和神经网络的无监督纹理分割

提出一种基于高斯-马尔可夫随机场(GMRF)和神经网络的无监督纹理分割方法,方法分为两步:第一步先将图像分为不重叠的小块,在小块中计算GMRF参数,并将此参数和该块的均值、方差作为该块的特征向量,然后进行聚类,得到原图像的一个初始分割和图像中所包含的类别数;第二步构造一个决定性松弛的神经网络,将第一步得到的结果作为初始输入,经过神经网络计算,得到一个精确的分割结果.实验证明:该方法是一种有效的纹理分割方法.     

A bayesian approach to classification of multiresolution remote sensing data

Several earth observation satellites acquire image bands with different spatial resolutions, e.g., a panchromatic band with high resolution and spectral bands with lower resolution. Likewise, we often face the problem of different resolutions when performing joint analysis of images acquired by different satellites. This work presents models and methods for classification of multiresolution images. The approach is based on the concept of a reference resolution, corresponding to the highest resolution in the dataset. Prior knowledge about the spatial characteristics of the classes is specified through a Markov random field model at the reference resolution. Data at coarser scales are modeled as mixed pixels by relating the observations to the classes at the reference resolution. A Bayesian framework for classification based on this multiscale model is proposed. The classification is realized by an iterative conditional modes (ICM) algorithm. The parameter estimation can be based both on a training set and on pixels with unknown class. A computationally efficient scheme based on a combination of the ICM and the expectation-maximization algorithm is proposed. Results obtained on simulated and real satellite images are presented.     

Segmentation of textured images using a multiresolution Gaussianautoregressive model

We present a new algorithm for segmentation of textured images using a multiresolution Bayesian approach. The new algorithm uses a multiresolution Gaussian autoregressive (MGAR) model for the pyramid representation of the observed image, and assumes a multiscale Markov random field model for the class label pyramid. The models used in this paper incorporate correlations between different levels of both the observed image pyramid and the class label pyramid. The criterion used for segmentation is the minimization of the expected value of the number of misclassified nodes in the multiresolution lattice. The estimate which satisfies this criterion is referred to as the "multiresolution maximization of the posterior marginals" (MMPM) estimate, and is a natural extension of the single-resolution "maximization of the posterior marginals" (MPM) estimate. Previous multiresolution segmentation techniques have been based on the maximum a posterior (MAP) estimation criterion, which has been shown to be less appropriate for segmentation than the MPM criterion. It is assumed that the number of distinct textures in the observed image is known. The parameters of the MGAR model-the means, prediction coefficients, and prediction error variances of the different textures-are unknown. A modified version of the expectation-maximization (EM) algorithm is used to estimate these parameters. The parameters of the Gibbs distribution for the label pyramid are assumed to be known. Experimental results demonstrating the performance of the algorithm are presented.     

Restriction of a Markov random field on a graph and multiresolutionstatistical image modeling

The association of statistical models and multiresolution data analysis in a consistent and tractable mathematical framework remains an intricate theoretical and practical issue. Several consistent approaches have been proposed previously to combine Markov random field (MRF) models and multiresolution algorithms in image analysis: renormalization group, subsampling of stochastic processes, MRFs defined on trees or pyramids, etc. For the simulation or a practical use of these models in statistical estimation, an important issue is the preservation of the local Markovian property of the representation at the different resolution levels. It is shown that this key problem may be studied by considering the restriction of a Markov random field (defined on some simple finite nondirected graph) to a part of its original site set. Several general properties of the restricted field are derived. The general form of the distribution of the restriction is given. “Locality” of the field is studied by exhibiting a neighborhood structure with respect to which the restricted field is an MRF. Sufficient conditions for the new neighborhood structure to be “minimal” are derived. Several consequences of these general results related to various “multiresolution” MRF-based modeling approaches in image analysis are presented     

Multiresolution texture segmentation with application to diagnostic ultrasound images

A multiresolution texture segmentation (MTS) approach to image segmentation that addresses the issues of texture characterization, image resolution, and time to complete the segmentation is presented. The approach generalizes the conventional simulated annealing method to a multiresolution framework and minimizes an energy function that is dependent on the resolution of the size of the texture blocks in an image. A rigorous experimental procedure is also proposed to demonstrate the advantages of the proposed MTS approach on the accuracy of the segmentation, the efficiency of the algorithm, and the use of varying features at different resolution. Semireal images, created by sampling a series of diagnostic ultrasound images of an ovary in vitro, were tested to produce statistical measures on the performance of the approach. The ultrasound images themselves were then segmented to determine if the approach can achieve accurate results for the intended ultrasound application. Experimental results suggest that the MTS approach converges faster and produces better segmentation results than the single-level approach.     

Noncausal Gauss Markov random fields: parameter structure andestimation

The parameter structure of noncausal homogeneous Gauss Markov random fields (GMRF) defined on finite lattices is studied. For first-order (nearest neighbor) and a special class of second-order fields, a complete characterization of the parameter space and a fast implementation of the maximum likelihood estimator of the field parameters are provided. For general higher order fields, tight bounds for the parameter space are presented and an efficient procedure for ML estimation is described. Experimental results illustrate the application of the approach presented and the viability of the present method in fitting noncausal models to 2-D data     

Bayesian decision feedback for segmentation of binary images

We present real-time algorithms for the segmentation of binary images modeled by Markov mesh random fields (MMRFs) and corrupted by independent noise. The goal is to find a recursive algorithm to compute the maximum a posteriori (MAP) estimate of each pixel of the scene using a fixed lookahead of D rows and D columns of the observations. First, this MAP fixed-lag estimation problem is set up and the corresponding optimal recursive (but computationally complex) estimator is derived. Then, both hard and soft (conditional) decision feedbacks are introduced at appropriate stages of the optimal estimator to reduce the complexity. The algorithm is applied to several synthetic and real images. The results demonstrate the viability of the algorithm both complexity-wise and performance-wise, and show its subjective relevance to the image segmentation problem.     

A Markov random field model-based approach to unsupervised texturesegmentation using local and global spatial statistics

Many studies have proven that statistical model-based texture segmentation algorithms yield good results provided that the model parameters and the number of regions be known a priori. In this correspondence, we present an unsupervised texture segmentation method that does not require knowledge about the different texture regions, their parameters, or the number of available texture classes. The proposed algorithm relies on the analysis of local and global second and higher order spatial statistics of the original images. The segmentation map is modeled using an augmented-state Markov random field, including an outlier class that enables dynamic creation of new regions during the optimization process. A Bayesian estimate of this map is computed using a deterministic relaxation algorithm. Results on real-world textured images are presented.     

可见光波段的窄带导模共振滤光片的设计

为了使导模共振滤光片能在可见光范围内表现出良好的滤光效果,根据严格耦合波理论和等效介质理论,提出基于半导体材料单晶氧化锌薄膜的亚波长导模共振光栅滤光片的结构设计。通过仿真分析可知,该滤光片在可见光范围内的475nm,530nm与650nm波长处,反射效率都达到了100%,旁带反射率低于4%,并且峰值带宽均小于0.3nm。结果表明,该滤光片能分别在可见光的红、绿、蓝波段表现出良好的滤光效果,可以作为三基色的滤光片,在彩色合成与调制中得到重要的应用。     

Estimating Gaussian Markov random field parameters in anonstationary framework: application to remote sensing imaging

In this paper, we tackle the problem of estimating textural parameters. We do not consider the problem of texture synthesis, but the problem of extracting textural features for tasks such as image segmentation. We take into account nonstationarities occurring in the local mean. We focus on Gaussian Markov random fields for which two estimation methods are proposed, and applied in a nonstationary framework. The first one consists of extracting conditional probabilities and performing a least square approximation. This method is applied to a nonstationary framework, dealing with the piecewise constant local mean. This framework is adapted to practical tasks when discriminating several textures on a single image. The blurring effect affecting edges between two different textures is thus reduced. The second proposed method is based on renormalization theory. Statistics involved only concern variances of Gaussian laws, leading to Cramer-Rao estimators. This method is thus especially robust with respect to the size of sampling. Moreover, nonstationarities of the local mean do not affect results. We then demonstrate that the estimated parameters allow texture discrimination for remote sensing data. The first proposed estimation method is applied to extract urban areas from SPOT images. Since discontinuities of the local mean are taken into account, we obtain an accurate urban areas delineation. Finally, we apply the renormalization based on method to segment ice in polar regions from AVHRR data.     

Segmentation of Gabor-filtered textures using deterministicrelaxation

A supervised texture segmentation scheme is proposed in this article. The texture features are extracted by filtering the given image using a filter bank consisting of a number of Gabor filters with different frequencies, resolutions, and orientations. The segmentation model consists of feature formation, partition, and competition processes. In the feature formation process, the texture features from the Gabor filter bank are modeled as a Gaussian distribution. The image partition is represented as a noncausal Markov random field (MRF) by means of the partition process. The competition process constrains the overall system to have a single label for each pixel. Using these three random processes, the a posteriori probability of each pixel label is expressed as a Gibbs distribution. The corresponding Gibbs energy function is implemented as a set of constraints on each pixel by using a neural network model based on Hopfield network. A deterministic relaxation strategy is used to evolve the minimum energy state of the network, corresponding to a maximum a posteriori (MAP) probability. This results in an optimal segmentation of the textured image. The performance of the scheme is demonstrated on a variety of images including images from remote sensing.     

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     

Unsupervised texture segmentation using multichannel decompositionand hidden Markov models

In this paper, we describe an automatic unsupervised texture segmentation scheme using hidden Markov models (HMMs). First, the feature map of the image is formed using Laws' micromasks and directional macromasks. Each pixel in the feature map is represented by a sequence of 4-D feature vectors. The feature sequences belonging to the same texture are modeled as an HMM. Thus, if there are M different textures present in an image, there are M distinct HMMs to be found and trained. Consequently, the unsupervised texture segmentation problem becomes an HMM-based problem, where the appropriate number of HMMs, the associated model parameters, and the discrimination among the HMMs become the foci of our scheme. A two-stage segmentation procedure is used. First, coarse segmentation is used to obtain the approximate number of HMMs and their associated model parameters. Then, fine segmentation is used to accurately estimate the number of HMMs and the model parameters. In these two stages, the critical task of merging the similar HMMs is accomplished by comparing the discrimination information (DI) between the two HMMs against a threshold computed from the distribution of all DI's. A postprocessing stage of multiscale majority filtering is used to further enhance the segmented result. The proposed scheme is highly suitable for pipeline/parallel implementation. Detailed experimental results are reported. These results indicate that the present scheme compares favorably with respect to other successful schemes reported in the literature.     

New fast smoothers for multiscale systems

We consider the smoothing problem for multiscale stochastic systems based on the wavelet transform. These models involve processes indexed by the nodes of a dyadic tree. Each level of the dyadic tree represents one scale or resolution of the process; therefore, moving upward on the tree divides the resolution by 2, whereas moving downward multiplies it by 2. The processes are built according to a recursion in scale from coarse to fine to which random details are added. To operate the change in scale, one must perform an interpolation. This is achieved using the QMF pair of operators attached to a wavelet transform. These models have proved to be of great value to capture textures or fractal-like processes as well as to perform multiresolution sensor fusion (an example of which is given here). Up to now however, only subclasses of multiscale systems were amenable to fast algorithms and through different formalisms: those relying on Haar's wavelet and those involving only one of the two wavelet interpolators. We provide here a unifying framework that handles any system based on orthogonal wavelets. A smoothing theory is presented to define the field of fast algorithms for Markov random fields and give intuition on how to design them. This theory reveals the difficulties arising with general multiscale systems. We then prove that orthogonality properties of wavelets are the gate to fastness