Textural Defect Segmentation Using a Fourier-Domain Maximum Likelihood Estimation Method

Abstract

When automatically inspecting textured surface defects, the most important step is to segment the defects from the background. For complicated textures, however, defect segmentation is still a challenging problem. In this paper, we use a Fourier-domain maximum likelihood estimator (FDMLE) based on the fractional Brownian motion (FBM) model to inspect surface defects of textile fabrics. From the experiments, we obtain good results for defect segmentation, and find the method's performance is invariant under geometric transformation.When automatically inspecting textured surface defects, the most important step is to segment the defects from the background. For textures with regular structures, we simply use the structural approach, but for complicated textures such as fabrics, we may obtain better inspection results with a statistical approach. Chetverikov [3] provided some methods for detecting textural defects. Some stochastic models such as M,~r-kov's random field are used to analyze the statistical properties of textures [5,17]. Matrix methods such as the co-occurrence matrix and the neighboring gray level dependent matrix are used to extract textural features for classification [6, 8, 21, 251. Transform-based methods, such as the wavelet transform, are used to characterize textures and locate defects [1,12,18,24,27,28]. Those previous works concentrated on the feature extraction of textures, not textures themselves.In 1967, Mandelbrot proposed a new method, fractal geometry, which provides a new mathematical description for natural textures [ 14]. When using fractal models, the most important procedure is to measure the fractal parameter (or the Hurst coefficient) H. Lately, fractal analysis has been applied to textile fabric inspection [4, 11, 19, 20. 261. Researchers used the box-counting method and the variance method to estimate the fractal parameter H. However, from their results [ 10,13], we see that those estimation methods do not perform well.Fractional Brownian motion (FBM) [ 13,15,16,22], which is the generalized form of ordinary Brownian motion, is one of the most useful fractal models for the random fractals found in nature. FBM is also suited to the evaluation of images involving a varying range of gray level values [2,7,9,13). FBM is a nonstationary process and is difficult to analyze, but its increment is a strictsense Gaussian stationary process that has been termed fractional Gaussian noise (t~N). Since the probability density function of FBM (and FGN) is well known, a maximum likelihood estimator (MLE) can be derived to estimate the fractal parameter H on a self-similar texture image [ 13], but the tedious computation makes it difficult for practical applications. In earlier work (Wen el al.[23]), we proposed a Fourier-domain FBM (FDMLE) method that saves more computation time than the conventional MLE. In this paper, we use the FDMLE method to estimate the fractal parameter H values of textile fabrics, and segment defects from the background textures based on the estimated H values. F...

Automated fabric defect detection—A review

“…The differential boxcounting method [13] used differences in computing non-overlapping copies of a set of images and the method gave satisfactory results in all ranges of fractal dimension. Recently, Bu et al [64] have compared with single fractal feature in [66] using four fractal features and support vector data description. In [64], it was tested with seven datasets of 14,378 defect-free and 3222 defective samples of plain and twill fabric of size 256 × 256.…”

“…Various textures were tested in [6] (7 sets) and [7] (8 sets). The only explicit detection result, given by Chiu et al [66], was Fourier-domain maximum likelihood estimator (FDMLE) which was based on a fractional Brownian motion model for detecting fabric surface defects. Four defective images of size 128 × 128 were shown to be successfully detected by FDMLE.…”

“…The method was invariant to geometric transformation such as rotation, position shift, gray-level shift and size rescaling of an image. Though all the methods in [2,6,7,66] were claimed to be successful in defect detection, their reliability was unknown.…”

Fractal analysis of surface roughness of montmorillonite clay self-supported films: Effects of exchanged cations and of mechanical tensile stress

“…Indeed, MLE are asymptotically efficient (unbiased and of minimal variance when the sample number is high) [27]. MLE has been successfully applied in many applications as for example bone microarchitecture analysis on radiographs [28] or textile analysis [29]. The strategy to estimate the H parameter by MLE is the following.…”

Adaptive detection of weft-knitted fabric defects based on machine vision system

“…Fabric images can also be transformed to frequency domains using Fourier transform or wavelet analysis. Fourier transform is utilized as an effective approach in the feature extraction effort, which enhances the detail information existed in high frequency coefficients (Carstensen, 2002;Chiu, Chou, Liaw, & Wen, 2002;Shady, Gowayed, Abouiiana, Youssef, & Pastore, 2006). Since Fourier transform does not provide, in general, sufficient information for defect detection and it provides analysis in the whole frequency domain only, Tsai (2000) and Jianli and Baoqi (2007) adopted the wavelet transform to characterize the fabric texture at multi-scale and multi-orientation which provided a promising way for the classification of fabric defects.…”