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Convex Analysisの二,三の進展について

IEEE International Conference on Image Processing

Automated computer-vision-based defect detection has received much attention with the increasing surface quality assurance demands for the industrial manufacturing of flat steels. This article attempts to present a comprehensive survey on surface defect detection technologies by reviewing about 120 publications over the last two decades for three typical flat steel products of con-casting slabs and hot- and cold-rolled steel strips. According to the nature of algorithms as well as image features, the existing methodologies are categorized into four groups: statistical, spectral, model-based, and machine learning. These works are summarized in this review to enable easy referral to suitable methods for diverse application scenarios in steel mills. Realization recommendations and future research trends are also addressed at an abstract level.

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Automated Visual Defect Detection for Flat Steel Surface: A Survey

This book serves as an introduction to the flourishing field of super-resolution imaging. It is a compiled volume, with different authors for each of its 14 chapters. While not having a strong outline or textbook format, the chapters group into several sections.

Super-Resolution Imaging

Clustering for hyperspectral images (HSIs) is a very challenging task due to its inherent complexity. In this paper, we propose a novel spectral–spatial sparse subspace clustering $(\text{S}^{4}\text{C})$ algorithm for hyperspectral remote sensing images. First, by treating each kind of land-cover class as a subspace, we introduce the sparse subspace clustering (SSC) algorithm to HSIs. Then, considering the spectral and spatial properties of HSIs, the high spectral correlation and rich spatial information of the HSIs are taken into consideration in the SSC model to obtain a more accurate coefficient matrix, which is used to build the adjacent matrix. Finally, spectral clustering is applied to the adjacent matrix to obtain the final clustering result. Several experiments were conducted to illustrate the performance of the proposed $\text{S}^{4}\text{C}$ algorithm.

Spectral–Spatial Sparse Subspace Clustering for Hyperspectral Remote Sensing Images

Image demosaicing and denoising are import steps of image signal processing. Sequential executions of demosaicing and denoising have essential drawbacks that they degrade the results of each other. Joint demosaicing and denoising overcomes the difficulties by solving the two problems in one model. This paper introduces a unified object function with hidden priors and a variant of ADMM to recover a full-resolution color image with a noisy Bayer input. Experimental results demonstrate that our method performs better than state-of-the-art methods in both PSNR comparison and human vision. In addition, our method is much more robust to variations of noise level.

Joint demosaicing and denoising of noisy bayer images with ADMM

Automatic surface detection for quality control has largely employed image processing techniques, for example in steel and fabric defect inspection There are rising demands in the quality control industry for defective image analysis to fulfill its vital role in visual inspection In this paper, we introduce an unsupervised method using a low-rank representation based on texture prior for detection of defects on natural surfaces and formulate the detection process as a novel weighted low-rank reconstruction model The first step of the proposed method estimates the texture prior to a given image by constructing a texture prior map where higher values indicate a higher probability of abnormality The second step of the proposed method detects the defect via low-rank decomposition with the help of the texture prior Experiments on synthetic and real images show that the proposed method is superior in terms of detection accuracy and competitive in computational efficiency with respect to the state-of-the-art methods in surface defect detection research This contribution is of particular interest for manufacturers (eg, steel and fabric) for which defect detection largely relies on manual inspection

Automatic Visual Defect Detection Using Texture Prior and Low-Rank Representation

—We consider a new family of regularizers, termedweighted sorted ‘ 1 norms (WSL1), which generalizes the recentlyintroduced octagonal shrinkage and clustering algorithm for re-gression (OSCAR) and also contains the ‘ 1 and ‘ 1 norms asparticular instances. We focus on a special case of the WSL1, thedecreasing WSL1 (DWSL1), where the elements of the argumentvector are sorted in non-increasing order and the weights are alsonon-increasing. In this paper, after showing that the DWSL1 isindeed a norm, we derive two key tools for its use as a regularizer:the dual norm and the Moreau proximity operator.Index Terms—Structured sparsity, sorted ‘ 1 norm, proximalsplitting algorithms. I. I NTRODUCTION In recent years, much research has been devoted not only tosparsity, but also to structured/group sparsity [1]. The OSCAR[2] is a convex regularizer, which was proposed to promotevariable/feature grouping; unlike other methods, it does notrequire previous knowledge of the group structure and it isnot tied to any particular order of the variables. The OSCARcriterion for linear regression with a quadratic loss functionhas the formmin

Decreasing Weighted Sorted ${\ell_1}$ Regularization

The ordered weighted $\ell_1$ norm (OWL) was recently proposed, with two different motivations: because of its good statistical properties as a sparsity promoting regularizer, and as generalization of the so-called {\it octagonal shrinkage and clustering algorithm for regression} (OSCAR). The OSCAR is a convex group-sparsity inducing regularizer, which does not require the prior specification of the group structure. Also recently, much interest has been raised by the atomic norm formulation of several regularizers, not only because it provides an new avenue for their theoretical characterization, but also because it is particularly well suited to a type of method known as {\it conditional gradient} (CG), or Frank-Wolfe, algorithm. In this paper, we derive the atomic formulation of the OWL and exploit this formulation to show how Tikhonov regularization schemes can be handled using state-of-the-art proximal splitting algorithms, while Ivanov regularization can be efficiently implemented via the Frank-Wolfe algorithm.

The Ordered Weighted $\ell_1$ Norm: Atomic Formulation, Dual Norm, and Projections.

The ordered weighted $\ell_1$ norm (OWL) was recently proposed, with two different motivations: its good statistical properties as a sparsity promoting regularizer; the fact that it generalizes the so-called {\it octagonal shrinkage and clustering algorithm for regression} (OSCAR), which has the ability to cluster/group regression variables that are highly correlated. This paper contains several contributions to the study and application of OWL regularization: the derivation of the atomic formulation of the OWL norm; the derivation of the dual of the OWL norm, based on its atomic formulation; a new and simpler derivation of the proximity operator of the OWL norm; an efficient scheme to compute the Euclidean projection onto an OWL ball; the instantiation of the conditional gradient (CG, also known as Frank-Wolfe) algorithm for linear regression problems under OWL regularization; the instantiation of accelerated projected gradient algorithms for the same class of problems. Finally, a set of experiments give evidence that accelerated projected gradient algorithms are considerably faster than CG, for the class of problems considered.

Xiangrong Zeng

Papers

Joint demosaicing and denoising of noisy bayer images with ADMM

Automatic Visual Defect Detection Using Texture Prior and Low-Rank Representation

Decreasing Weighted Sorted ${\ell_1}$ Regularization

The Ordered Weighted $\ell_1$ Norm: Atomic Formulation, Dual Norm, and Projections.

The Ordered Weighted $\ell_1$ Norm: Atomic Formulation, Projections, and Algorithms