Defect Detection for Patterned Fabric Images Based on GHOG and Low-Rank Decomposition

In contrast to defect-free fabric images with macro-homogeneous textures and regular patterns, the fabric images with the defect are characterized by the defect regions that are salient and sparse among the redundant background. Therefore, as an effective tool for separating an image into a redundant part (the background) and sparse part (the defect), the low-rank decomposition model provides an ideal solution for patterned fabric defect detection. In this paper, a novel patterned method for fabric defect detection is proposed based on a novel texture descriptor and the low-rank decomposition model. First, an efficient second-order orientation-aware descriptor, denoted as GHOG, is designed by combining Gabor and histogram of oriented gradient (HOG). In addition, a spatial pooling strategy based on human vision mechanism is utilized to further improve the discrimination ability of the proposed descriptor. The proposed texture descriptor can make the defect-free image blocks lay in a low-rank subspace, while the defective image blocks have deviated from this subspace. Then, a constructed low-rank decomposition model divides the feature matrix generated from all the image blocks into a low-rank part, which represents the defect-free background, and a sparse part, which represents sparse defects. In addition, a non-convex log det as a smooth surrogate function is utilized to improve the efficiency of the constructed low-rank model. Finally, the defects are localized by segmenting the saliency map generated by the sparse matrix. The qualitative results and quantitative evaluation results demonstrate that the proposed method improves the detection accuracy and self-adaptivity comparing with the state-of-the-art methods

Applied Mathematics and Computational Physics

As faster and more efficient numerical algorithms become available, the understanding of the physics and the mathematical foundation behind these new methods will play an increasingly important role. This Special Issue provides a platform for researchers from both academia and industry to present their novel computational methods that have engineering and physics applications

BagStack Classification for Data Imbalance Problems with Application to Defect Detection and Labeling in Semiconductor Units

abstract: Despite the fact that machine learning supports the development of computer vision applications by shortening the development cycle, finding a general learning algorithm that solves a wide range of applications is still bounded by the ”no free lunch theorem”. The search for the right algorithm to solve a specific problem is driven by the problem itself, the data availability and many other requirements. Automated visual inspection (AVI) systems represent a major part of these challenging computer vision applications. They are gaining growing interest in the manufacturing industry to detect defective products and keep these from reaching customers. The process of defect detection and classification in semiconductor units is challenging due to different acceptable variations that the manufacturing process introduces. Other variations are also typically introduced when using optical inspection systems due to changes in lighting conditions and misalignment of the imaged units, which makes the defect detection process more challenging. In this thesis, a BagStack classification framework is proposed, which makes use of stacking and bagging concepts to handle both variance and bias errors. The classifier is designed to handle the data imbalance and overfitting problems by adaptively transforming the multi-class classification problem into multiple binary classification problems, applying a bagging approach to train a set of base learners for each specific problem, adaptively specifying the number of base learners assigned to each problem, adaptively specifying the number of samples to use from each class, applying a novel data-imbalance aware cross-validation technique to generate the meta-data while taking into account the data imbalance problem at the meta-data level and, finally, using a multi-response random forest regression classifier as a meta-classifier. The BagStack classifier makes use of multiple features to solve the defect classification problem. In order to detect defects, a locally adaptive statistical background modeling is proposed. The proposed BagStack classifier outperforms state-of-the-art image classification techniques on our dataset in terms of overall classification accuracy and average per-class classification accuracy. The proposed detection method achieves high performance on the considered dataset in terms of recall and precision.Dissertation/ThesisDoctoral Dissertation Computer Engineering 201

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Coupled Gradient Enhanced Damage - Viscoplasticity Model Using Phase Field Method

The aim of this dissertation is developing a framework to describe damage evolution as a phase transformation in solid materials and couple it to the well-known Perzyna type viscoplastic model to account for inelastic behavior of ductile materials. To accomplish this task, the following steps have been performed. First, a new nonlocal, gradient based damage model is proposed for isotropic elastic damage using the phase field method in order to show the evolution of damage in brittle materials. The general framework of the phase field model (PFM) is discussed and the order parameter is related to the damage variable in continuum damage mechanics (CDM). The time dependent Ginzburg-Landau equation which is also termed the Allen-Cahn equation is used to describe the damage evolution process. Specific length scale which addresses the transition region in which the process of changing the undamaged solid to the fully damaged material (microcracks) occurs is defined in order to capture the effect of the damaged localization zone. A new implicit damage variable is proposed through the phase field theory. Finite Difference Method is used and details of the different aspects and regularization capabilities are illustrated by means of numerical examples and the validity and usefulness of the phase field modeling approach is demonstrated. Subsequently, the theory is developed to address the anisotropic damage evolution and simulation in materials. The anisotropic damage is discussed and appropriate nonconserved order parameters in three mutually perpendicular directions are defined to find the growth of the components of a second order diagonal damage tensor corresponding to the principle directions of a general second order damage tensor. In contrast to the previous models, two new tensors are proposed to act as interpolation and potential functions along with three coupled Allen - Cahn equations in order to obtain the evolution of the order parameters, which is the basis of the definition of the damage rate. The tensor formulation of the growth of the components of the damage tensor using the phase field theory is proposed for the first time. It is shown that by introducing a set of material parameters, there is a robust and simplified way to model the nonlocal behavior of damage and predict the corresponding material behavior along the principal axes of the second order damage tensor. Finally, the framework of coupled nonlocal damage model through phase field method and viscoplasticity in continuum scale is developed. It is shown that the recently proposed non local gradient type damage model through the phase field method can be coupled to a viscoplastic model to capture the inelastic behavior of the rate dependent material. Free energy functional of the system containing two main parts including damage propagation as a phase transformation and viscoplastic deformation is proposed. Analogous to conventional viscoplastic models, two terms are incorporated in the viscoplastic free energy functional to appropriately address dissipation and the von Mises type viscoplastic surface. In this framework it is assumed that the damage variable covers summation of evolution of microcracks density in elastic and plastic region and the total strain represents the summation of the elastic and viscoplastic counterparts. Since all the examples of chapters two and three are solved using the Finite Element Method, appropriate algorithms and derivations are also summarized in the last chapter