Multiple resolution segmentation of textured images

A multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior. In addition, an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions. Both algorithms use a causal Gaussian autoregressive model to describe the mean, variance, and spatial correlation of the image textures. Together, the algorithms can be used to perform unsupervised texture segmentation. The multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified. This method results in accurate segmentations and requires significantly less computation than some previously known methods. The field containing the classification of each pixel in the image is modeled as a Markov random field. Segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint. At each resolution, the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks. The unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the AIC information criterion. Clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters. Concurrently, the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached     

基于Markov随机场模型的纹理图像的缺陷检测

在工业自动化研究中,部件的缺陷检测是非常重要的过程。文中提出了一种基于图像纹理分析的表面缺陷检测方法,图像表面纹理特征是利用Markov随机场模型来描述的,通过学习和聚类分析来检测出纹理图像中有缺陷的区域。试验结果表明,该方法可以有效地描述不同种物质表面的纹理特征,并能准确地检测和定位缺陷。     

Gibbs Random Fields,Fuzzy Clustering,and the Unsupervised Segmentation of Textured Images

In this paper we present an unsupervised segmentation strategy for textured images, based on a hierarchical model in terms of discrete Markov Random Fields. The textures are modeled as Gaussian Gibbs Fields, while the image partition is modeled as a Markov Mesh Random Field. The segmentation is achieved in two phases: the first one consists of evaluating, from disjoint blocks which are classified as homogeneous, the model parameters for each texture present in the image. This unsupervised learning phase uses a fuzzy clustering procedure, applied to the features extracted from every pixel block, to determine the number of textures in the image and to roughly locate the corresponding regions. The second phase consists of the fine segmentation of the image, using Bayesian local decisions based on the previously obtained model parameters. The originality of the proposed approach lies in the three following aspects: (1) the Gibbs distribution corresponding to each texture type is expressed in terms of its canonical potential. This formulation leads to a compact formulation of the global field energy, in terms of the marginal probabilities over pixel cliques. A similar expression is also introduced in the partition model. Such formulations lead to the decomposition of the segmentation problem into a set of local statistical decisions; (2) the segmentation strategy consists of an unsupervised estimation, in which the model parameters are evaluated directly from the observation, by means of a fuzzy clustering technique; (3) no arbitrary assumption is made concerning the number of textures present. Rather, the fuzzy clustering procedure used to estimate the model parameters is applied in a hierarchical manner, searching for a cluster configuration of maximum plausibility.     

Unsupervised segmentation of Markov random field modeled texturedimages using selectionist relaxation

Among the existing texture segmentation methods, those relying on Markov random fields have retained substantial interest and have proved to be very efficient in supervised mode. The use of Markov random fields in unsupervised mode is, however, hampered by the parameter estimation problem. The recent solutions proposed to overcome this difficulty rely on assumptions about the shapes of the textured regions or about the number of textures in the input image that may not be satisfied in practice. In this paper, an evolutionary approach, selectionist relaxation, is proposed as a solution to the problem of segmenting Markov random field modeled textures in unsupervised mode. In selectionist relaxation, the computation is distributed among a population of units that iteratively evolves according to simple and local evolutionary rules. A unit is an association between a label and a texture parameter vector. The units whose likelihood is high are allowed to spread over the image and to replace the units that receive lower support from the data. Consequently, some labels are growing while others are eliminated. Starting with an initial random population, this evolutionary process eventually results in a stable labelization of the image, which is taken as the segmentation. In this work, the generalized Ising model is used to represent textured data. Because of the awkward nature of the partition function in this model, a high-temperature approximation is introduced to allow the evaluation of unit likelihoods. Experimental results on images containing various synthetic and natural textures are reported     

A Model-Based Method for Rotation Invariant Texture Classification

This paper presents a new model-based approach for texture classification which is rotation invariant, i.e., the recognition accuracy is not affected if the orientation of the test texture is different from the orientation of the training samples. The method uses three statistical features, two of which are obtained from a new parametric model of the image called a ``circular symmetric autoregressive model.' Two of the proposed features have physical interpretation in terms of the roughness and directionality of the texture. The results of several classification experiments on differently oriented samples of natural textures including both microtextures and macrotextures are presented.     

MRF model and FRAME model-based unsupervised image segmentation

This paper presents a method for unsupervised segmentation of images consisting of multiple textures. The images under study are modeled by a proposed hierarchical random field model, which has two layers. The first layer is modeled as a Markov Random Field (MRF) representing an unobservable region image and the second layer uses "Filters, Random and Maximum Entropy (Abb. FRAME)" model to represent multiple textures which cover each region. Compared with the traditional Hierarchical Markov Random Field (HMRF), the FRAME can use a bigger neighborhood system and model more complex patterns. The segmentation problem is formulated as Maximum a Posteriori (MAP) estimation according to the Bayesian rule. The iterated conditional modes (ICM) algorithm is carried out to find the solution of the MAP estimation. An algorithm based on the local entropy rate is proposed to simplify the estimation of the parameters of MRF. The parameters of FRAME are estimated by the ExpectationMaximum (EM) algorithm. Finally, an exp     

形态小波域多尺度马尔可夫模型在纹理图像分割中的应用

针对图像分割中小波域多尺度马尔可夫模型(MRMRF-W)无法有效描述图像非线性特征,提出了一种在形态小波域下的多尺度MRF模型（MRMRF-MW）,实现纹理图像分割。该模型结合了形态小波和MRF各自的优势,能够对图像进行非线性多尺度分解,并在各尺度上进行空间关系建模。通过对两个纹理图像库（Brodatz纹理库、Prague纹理库）中图像的分割实验,验证了该模型的有效性。     

基于无参数Markov随机场模型的彩色纹理综合方法

提出一种基于多尺度、无参数Markov随机场模型和KL变换的彩色纹理综合方法。该方法能捕捉原始纹理的高阶统计特性,综合出与原始纹理视觉一致的彩色纹理图像。实验结果证明该方法对彩色纹理图像的综合非常有效。     

Synthesis of Color Textures for Multimedia Applications

An algorithm for synthesizing color textures from a small set of parameters is presented in this paper. The synthesis algorithm is based on the 2-D moving average model, and realistic textures resembling many real textures can be synthesized using this algorithm. A maximum likelihood estimation algorithm to estimate parameters from a sample texture is also presented. By combining the estimation and synthesis algorithms, a color texture can be synthesized from a sample texture without human intervention. Using the estimated parameters, a texture larger than the original image can be synthesized from a small texture sample. The synthesis algorithm does not require an expensive iterative algorithm, and the quality of synthesized textures may be acceptable for many multimedia applications. In the experiment, various textures suitable for multimedia applications are synthesized from parameters estimated from real textures.     

Random field identification from a sample: Experimental results

In this report, we consider the problem of identifying a random field belonging to a given class, given sample generation by that random field. We take the field to be from one of two special classes: stationary fields of independent samples and fields that are simple stationary Markov chains. Interval estimators for the parameters of the field are derived from the joint frequencies of occurrence of elements of the sample. We use Monte Carlo simulations to evaluate the performance of these estimators and to investigate the tightness of some theoretical bounds for their confidence levels. We also demonstrate how these methods can be applied to the problem of texture classification or segmentation, and present examples of textures distinguishable using these methods but not distinguishable to the eye.     

Texture boundary detection based on the long correlation model

The problem of detecting texture boundaries without assuming any knowledge on the number of regions or the types of textures is considered. Texture boundaries are often regarded as better features than intensity edges, because a large class of images can be considered a composite of several different texture regions. An algorithm is developed that detects texture boundaries at reasonably high resolution without assuming any prior knowledge on the texture composition of the image. The algorithm utilizes the long correlation texture model with a small number of parameters to characterize textures. The parameters of the model are estimated by a least-squares method in the frequency domain. The existence and the location of texture boundary is estimated by the maximum-likelihood method. The algorithm is applied to several different images, and its performance is shown by examples. Experimental results show that the algorithm successfully detects texture boundaries without knowing the number of types of textures in the image     

Local surface shape estimation of 3-D textured surfaces usingGaussian Markov random fields and stereo windows

The problem of extracting the local shape information of a 3-D texture surface from a single 2-D image by tracking the perceived systematic deformations the texture undergoes by virtue of being present on a 3-D surface and by virtue of being imaged is examined. The surfaces of interest are planar and developable surfaces. The textured objects are viewed as originating by laying a rubber planar sheet with a homogeneous parent texture on it onto the objects. The homogeneous planar parent texture is modeled by a stationary Gaussian Markov random field (GMRF). A probability distribution function for the texture data obtained by projecting the planar parent texture under a linear camera model is derived, which is an explicit function of the parent GMRF parameters, the surface shape parameters. and the camera geometry. The surface shape parameter estimation is posed as a maximum likelihood estimation problem. A stereo-windows concept is introduced to obtain a unique and consistent parent texture from the image data that, under appropriate transformations, yields the observed texture in the image. The theory is substantiated by experiments on synthesized as well as real images of textured surfaces     

Bayesian estimation for homogeneous and inhomogeneous Gaussianrandom fields

This paper investigates Bayesian estimation for Gaussian Markov random fields. In particular, a new class of compound model is proposed which describes the observed intensities using an inhomogeneous model and the degree of spatial variation described by a second random field. The coupled Markov random fields are used as prior distributions, and combined with Gaussian noise models to produce posterior distributions on which estimation is based. All model parameters are estimated, in a fully Bayesian setting, using the Metropolis-Hasting algorithm. The full posterior estimation procedures are illustrated and compared using various artificial examples. For these examples the inhomogeneous model performs very favorably when compared to the homogeneous model, allowing differential degrees of smoothing and varying local textures     

Image denoising based on hierarchical Markov random field

We propose a hierarchical Markov random field model-based method for image denoising in this paper. The method employs a Markov random field (MRF) model with three layers. The first layer represents the underlying texture regions. The second layer represents the noise free image. And the third layer is the observed noisy image. Iterated conditional modes (ICM) is used to find the maximum a posteriori (MAP) estimation of the noise free image and texture region field. The experimental results show that the new method can effectively suppress additive noise and restore image details.     

Multispectral random field models for synthesis and analysis ofcolor images

Multispectral extensions to the traditional gray level simultaneous autoregressive (SAR) and Markov random field (MRF) models are considered. Furthermore, a new image model is proposed, the pseudo-Markov model, which retains the characteristics of the multispectral Markov model, yet admits to a simplified parameter estimation method. These models are well-suited to analysis and modeling of color images. For each model considered, procedures are developed for parameter estimation and image synthesis. Experimental results, based on known image models and natural texture samples, substantiate the validity of thee results     

Unsupervised image segmentation using a simple MRF model with a new implementation scheme

A simple Markov random field model with a new implementation scheme is proposed for unsupervised image segmentation based on image features. The traditional two-component MRF model for segmentation requires training data to estimate necessary model parameters and is thus unsuitable for unsupervised segmentation. The new implementation scheme solves this problem by introducing a function-based weighting parameter between the two components. Using this method, the simple MRF model is able to automatically estimate model parameters and produce accurate unsupervised segmentation results. Experiments demonstrate that the proposed algorithm is able to segment various types of images (gray scale, color, texture) and achieves an improvement over the traditional method.     

An efficient texture image segmentation algorithm based on the GMRF model for classification of remotely sensed imagery

Texture analysis of remote sensing images based on classification of area units represented in image segments is usually more accurate than operating on an individual pixel basis. In this paper we suggest a two-step procedure to segment texture patterns in remotely sensed data. An image is first classified based on texture analysis using a multi-parameter and multi-scale technique. The intermediate results are then treated as initial segments for subsequent segmentation based on the Gaussian Markov random field (GMRF) model. The segmentation procedure seeks to merge pairs of segments with the minimum variance difference. Experiments using real data prove that the two-step procedure improves both computational efficiency and accuracy of texture classification.     

Generating connected textured fractal patterns using Markov randomfields

An algorithm that yields textured and connected binary fractals is presented. The texture is imposed by modelling the fractal as a Markov random field (MRF) at every resolution level. The model size and the parameters specify the texture. The generation starts at a coarser level and continues at finer levels. Connectivity, which is a global property, is maintained by restricting the flow of the sample generating Markov chain within a limited subset of all possible outcomes of the Markov random field. The texture is controlled by the parameters of the MRF model being used. Sample patterns are shown     

A theoretical comparison of texture algorithms

An evaluation of the ability of four texture analysis algorithms to perform automatic texture discrimination will be described. The algorithms which will be examined are the spatial gray level dependence method (SGLDM), the gray level run length method (GLRLM), the gray level difference method (GLDM), and the power spectral method (PSM). The evaluation procedure employed does not depend on the set of features used with each algorithm or the pattern recognition scheme. Rather, what is examined is the amount of texturecontext information contained in the spatial gray level dependence matrices, the gray level run length matrices, the gray level difference density functions, and the power spectrum. The comparison will be performed in two steps. First, only Markov generated textures will be considered. The Markov textures employed are similar to the ones used by perceptual psychologist B. Julesz in his investigations of human texture perception. These Markov textures provide a convenient mechanism for generating certain example texture pairs which are important in the analysis process. In the second part of the analysis the results obtained by considering only Markov textures will be extended to all textures which can be represented by translation stationary random fields of order two. This generalization clearly includes a much broader class of textures than Markovian ones. The results obtained indicate that the SGLDM is the most powerful algorithm of the four considered, and that the GLDM is more powerful than the PSM.