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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...

Signature verification is one of the biometric techniques frequently used for personal identification. In many commercial scenarios, such as bank check payment, the signature verification process is based on human examination of a single known sample. Although there is extensive research on automatic signature verification, yet few attempts have been made to perform the verification based on a single reference sample. In this paper, we propose an off-line handwritten signature verification method based on an explainable deep learning method (deep convolutional neural network, DCNN) and unique local feature extraction approach. We use the open-source dataset, Document Analysis and Recognition (ICDAR) 2011 SigComp, to train our system and verify a questioned signature as genuine or a forgery. All samples used in our testing process are collected from a new author whose signatures are not present in the training or other stages. From the experimental results, we get the accuracy between 94.37% and 99.96%, false rejection rate (FRR) between 5.88% and 0%, false acceptance rate (FAR) between 0.22% and 5.34% in our testing dataset.