A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature <s> BIB001 </s> A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> The authors discuss the problem of textile fabric inspection using the visual textural properties of the fabric. The problem is to detect and locate the various kinds of defects that might be present in a given fabric sample based on an image of the fabric. Stochastic models are used to model the visual fabric texture. The authors use the Gaussian Markov random field to model the texture image of nondefective fabric. The inspection problem is cast as a statistical hypothesis testing problem on statistics derived from the model. The image of the fabric patch to be inspected is partitioned into nonoverlapping windows of size N*N where each window is classified as defective or nondefective based on a likelihood ratio test of size alpha . The test is recast in terms of the sufficient statistics associated with the model parameters. The sufficient statistics are easily computable for any sample. The authors generalize the test when the model parameters of the fabric are assumed to be unknown. > <s> BIB002 </s> A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> Abstract We present a multiresolution simultaneous autoregressive (MR-SAR) model for texture classification and segmentation. First, a multivariate rotation-invariant SAR (RISAR) model is introduced which is based on the circular autoregressive (CAR) model. Experiments show that the multivariate RISAR model outperforms the CAR model in texture classification. Then, we demonstrate that integrating the information extracted from multiresolution SAR models gives much better performance than single resolution methods in both texture classification and texture segmentation. A quality measure to evaluate individual features for the purpose of segmentation is also presented. We employ the spatial coordinates of the pixels as two additional features to remove small speckles in the segmented image, and carefully examine the role that the spatial features play in texture segmentation. Two internal indices are introduced to evaluate the unsupervised segmentation and to find the “true” number of segments or clusters existing in the textured image. <s> BIB003 </s> A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> Abstract Textural features for pattern recognition are compared. The problem addressed is to determine which features optimize classification rate. Such features may be used in image segmentation, compression, inspection, and other problems in computer vision. Many textural features have been proposed in the literature. No large-scale objective comparative study has appeared. The goal is comparing and evaluating in a quantitative manner four types of features, namely Markov Random Field parameters, multi-channel filtering features, fractal based features, and co-occurrence features. Performance is assessed by the criterion of classification error rate with a Nearest Neighbor classifier and the Leave-One-Out estimation method using forward selection. Four types of texture are studied, two synthetic (fractal and Gaussian Markov Random Fields) and two natural (leather and painted surfaces). The results show that co-occurrence features perform best followed by the fractal features. However, there is no universally best subset of features. The feature selection task has to be performed for each specific problem to decide which feature of which type one should use. <s> BIB004 </s> A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> 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. <s> BIB005 </s> A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> Texture analysis plays an important role in the automated visual inspection of textured images to detect their defects. For this purpose, model-based and feature-based methods are implemented and tested for textile images in a laboratory environment. The methods are compared in terms of their success rates in determining the defects. The Markov Random Field model is applied on different DSP systems for real-time inspection. <s> BIB006 </s> A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> This work presents an application of software engineering to fabric inspection. An inspection system has been developed for textile industries that aims automatic failure detection. Such as wood, paper and steel industries, this environment has particular characteristics in which surface defect detection is used for quality control. This system combines concept from software engineering and decision support. Detection of defects within the inspected texture is performed in a first step acquiring images by CCD cameras, then extracting texture features and, finally by classifiers being trained a priori on database of defective and non-defective samples. The extracted data depend on the type of method selected for image analysis. The used types are based on segmentation or fractal dimension. Two usual segmentation techniques were adapted and improved. A new algorithm was developed to calculate efficiently fractal dimension of textures. Experiments show the accuracy and applicability of the proposed techniques for a real factory environment. <s> BIB007 </s> A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> We present novel simple appearance and shape models that we call epitomes. The epitome of an image is its miniature, condensed version containing the essence of the textural and shape properties of the image. As opposed to previously used simple image models, such as templates or basis functions, the size of the epitome is considerably smaller than the size of the image or object it represents, but the epitome still contains most constitutive elements needed to reconstruct the image. A collection of images often shares an epitome, e.g., when images are a few consecutive frames from a video sequence, or when they are photographs of similar objects. A particular image in a collection is defined by its epitome and a smooth mapping from the epitome to the image pixels. When the epitomic representation is used within a hierarchical generative model, appropriate inference algorithms can be derived to extract the epitome from a single image or a collection of images and at the same time perform various inference tasks, such as image segmentation, motion estimation, object removal and super-resolution. <s> BIB008 </s> A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> We present a new approach to detecting defects in random textures which requires only very few defect free samples for unsupervised training. Each product image is divided into overlapping patches of various sizes. Then, density mixture models are applied to reduce groupings of patches to a number of textural exemplars, referred to here as texems, characterising the means and covariances of whole sets of image patches. The texems can be viewed as implicit representations of textural primitives. A multiscale approach is used to save computational costs. Finally, we perform novelty detection by applying the lower bound of normal samples likelihoods on the multiscale defect map of an image to localise defects. <s> BIB009 </s> A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> A novel method is presented to detect defects in random colour textures which requires only a very few normal samples for unsupervised training. We decorrelate the colour image by generating three eigenchannels in each of which the surface texture image is divided into overlapping patches of various sizes. Then, a mixture model and EM is applied to reduce groupings of patches to a small number of textural exemplars, or texems. Localised defect detection is achieved by comparing the learned texems to patches in the unseen image eigenchannels. <s> BIB010 </s> A Review of Recent Advances in Surface Defect Detection using Texture analysis Techniques <s> Model based approaches <s> We present an approach to detecting and localizing defects in random color textures which requires only a few defect free samples for unsupervised training. It is assumed that each image is generated by a superposition of various-size image patches with added variations at each pixel position. These image patches and their corresponding variances are referred to here as textural exemplars or texems. Mixture models are applied to obtain the texems using multiscale analysis to reduce the computational costs. Novelty detection on color texture surfaces is performed by examining the same-source similarity based on the data likelihood in multiscale, followed by logical processes to combine the defect candidates to localize defects. The proposed method is compared against a Gabor filter bank-based novelty detection method. Also, we compare different texem generalization schemes for defect detection in terms of accuracy and efficiency. <s> BIB011
Model based methods include, among many others, fractal models BIB001 , autoregressive models BIB003 BIB005 , random field models  , the epitome model BIB008 , and the texem model BIB011 . Fractals, initially proposed by Mandelbrot BIB001 , are geometric primitives that are self-similar and irregular in nature. Fragments of a fractal object are exact or statistical copies of the whole object and they can match the whole by stretching and shifting. Fractal dimension and lacunarity are the most important measurements in fractal models. The former servs as a measure of complexity and irregularity; and the latter measures the structural variation or inhomogeneity. In  BIB007 , Conci and Proenca used box counting to extract fractal features for detecting defects in fabric images. In a comparative study by Ohanian and Dubes BIB004 , the fractal method performed reasonably well against co-occurrence matrices, Gabor filters, and Markov random fields in texture classification. However, it has achieved limited success in real applications. Fractals can have the same fractal dimension but look completely different. Fractal models are mainly suitable for natural textures where self-similarity may hold. MRF theory provides a convenient and consistent way for modelling context dependent entities such as pixels, through characterising mutual influences among such entities using conditional MRF distributions  . The establishment of the equivalence between MRFs and Gibbs distribution   provided tractable means for statistical analysis as Gibbs distribution takes a much simpler form. In BIB002 , Cohen et al. used Gaussian Markov Random Fields (GMRF) to model defect free textile web. The inspection process was treated as a hypothesis testing problem on the statistics derived from the GMRF model. The testing image was partitioned into non-overlapping sub-blocks, where each window was then classified as defective or non-defective. Baykut et al. BIB006 implemented this method in a real-time application with a dedicated DSP system. In  , the authors showed that MRF based methods were competitive in a comparative study against other statistical and spectral based methods in defect detection. Very recently, Xie and Mirmehdi BIB009 BIB010 BIB011 proposed a novel statistical model, called texture exemplars or texems, to represent and analyse random textures. In a two-layer structure, a texture image, as the first layer, is considered to be a superposition of a number of texture exemplars, possibly overlapped, from the second layer. Each texture exemplar, or simply texem, is characterised by mean values and corresponding covariances. Each set of these texems may comprise various sizes from different image scales. Different Gaussian mixture models were explored to learn these texem representations. Similar to the epitome model BIB008 , only raw pixel values are used instead of filtering responses. However, unlike the epitome the texem model does not enforce the texture primitives condensing to a single image patch. The model was applied to localise defects on random textured ceramic tile surfaces and showed significant improvements compared against Gabor filtering based methods in a novelty detection framework.