High-order data are modeled using matrices whose entries are numerical arrays of a fixed size. These arrays, called t-scalars, form a commutative ring under the convolution product. Matrices with elements in the ring of t-scalars are referred to as t-matrices. The t-matrices can be scaled, added and multiplied in the usual way. There are t-matrix generalizations of positive matrices, orthogonal matrices and Hermitian symmetric matrices. With the t-matrix model, it is possible to generalize many well-known matrix algorithms. In particular, the t-matrices are used to generalize the singular value decomposition (SVD), high-order SVD (HOSVD), principal component analysis (PCA), two-dimensional PCA (2DPCA) and Grassmannian component analysis (GCA). The generalized t-matrix algorithms, namely TSVD, THOSVD, TPCA, T2DPCA and TGCA, are applied to low-rank approximation, reconstruction and supervised classification of images. Experiments show that the t-matrix algorithms compare favorably with standard matrix algorithms.

Purpose -Fabric defect detection plays an important role in textile quality control. The purpose of this paper is to propose a fabric defect detection algorithm via context-based local texture saliency analysis. Design/methodology/approach -In the proposed algorithm, a target image is first divided into blocks, then the Local Binary Pattern (LBP) technique is used to extract the texture features of blocks. Second, for a given image block, several other blocks are randomly chosen for calculating the LBP contrast between a given block and the randomly chosen blocks. Based on the obtained contrast information, a saliency map is produced. Finally, saliency map is segmented by using an optimal threshold, which is obtained by an iterative approach. Findings -The experimental results show that the proposed algorithm, integrating local texture features and global image texture information, can detect texture defects effectively. Originality/value -In this paper, a novel fabric defect detection algorithm via context-based local texture saliency analysis is proposed.

We consider the tensor-based spectral-spatial feature extraction problem for hyperspectral image classification. First, a tensor framework based on circular convolution is proposed. Based on this framework, we extend the traditional PCA to its tensorial version TPCA, which is applied to the spectral-spatial features of hyperspectral image data. The experiments show that the classification accuracy obtained using TPCA features is significantly higher than the accuracies obtained by its rivals.

Semi-fragile self-recoverable watermarking algorithms are important to meet various requirements such as security, robustness, localization, and image recovery. However, current approaches are not adequate for this importance. Thus, we propose a novel semi-fragile and self-recoverable watermarking algorithm based on a group quantization and double authentication method. In the proposed algorithm, a target image is first split into 16×16 image blocks. For each image block, a five-bit authentication watermark is generated from the first-order statistical moment of the block and then is embedded into the mid-frequency band of another image block by a novel groupbased wavelet quantization method. With the generated watermarks, image security is enhanced by randomly permuting coefficients among a group and image robustness is improved by embedding the watermark in the largest coefficient inside a sub-group by significant difference parity quantization. The proposed double authentication ring structure effectively improves the image localization accuracy. Recovered image is a better approximate to the original image. Experimental comparisons of ours with other algorithms shows the effectiveness of the proposed self-recoverable and semi-fragile watermarking algorithm.

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We consider the feature extraction problem based on compressive sampling for supervised image classification. Inspired by recently emerged 1D compressive sampling (1DCS) and 2DPCA techniques, a novel 2D compressive sampling method, called 2DCS, using two random underdetermined projections, is proposed. 2DCS data could be effectively used for pattern representation. Moreover, original data could be exactly reconstructed from 2DCS compression. The proposed method is efficient for feature extraction and data compression, and, compared with 1DCS and 2DPCA, requires lower computational complexity. Combined with the sophisticated classifiers, the efficacy of supervised image classification could be improved. Experimental results show the superiorities of the proposed algorithm.

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We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each class is modeled by a union of of a finite number of affine subspaces of the feature space. The affine subspaces have a common dimension, which is assumed to be much less than the dimension of the feature space. The subspaces are found using regression based on the 0 -norm. The proposed method is a generalisation of classical NN (Nearest Neighbor), NFL (Nearest Feature Line) classifiers and has a close relationship to NS (Nearest Subspace) classifier. The proposed classifier with an accurately estimated dimension parameter generally outperforms its competitors in terms of classification accuracy. We also propose a fast version of the classifier using a neighborhood representation to reduce its computational complexity. Experiments on publicly available datasets corroborate these claims.