From Grayscale to Color: Quaternion Linear Regression for Color Face Recognition

Zou, Cuiming; Kou, Kit Ian; Dong, Li; Zheng, Xianwei; Tang, Yuan Yan

doi:10.1109/access.2019.2948937

Cited by 22 publications

(11 citation statements)

References 33 publications

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“…Quaternions form a finitedimensional non-commutative algebra generalizing the field of complex numbers. Quaternion matrices and tensors are used in histopathological image analysis [22], image & video recovery and representations [23]- [25], color image denoising [26], [27], color face recognition [28], [29], color image inpainting [30], [31], to name a few.…”

Section: A Backgroundsmentioning

confidence: 99%

Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra

Liao¹,

Shen²,

Li³

et al. 2022

Preprint

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Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order input into a matrix or break it into a series of order-two slices to tackle higher order data such as multispectral images and videos with the SVD. Higher order singular value decomposition (HOSVD) extends the SVD and can approximate higher order data using sums of a few rank-one components. We consider the problem of generalizing HOSVD over a finite dimensional commutative algebra. This algebra, referred to as a t-algebra, generalizes the field of complex numbers. The elements of the algebra, called t-scalars, are fix-sized arrays of complex numbers. One can generalize matrices and tensors over t-scalars and then extend many canonical matrix and tensor algorithms, including HOSVD, to obtain higher-performance versions. The generalization of HOSVD is called THOSVD. Its performance of approximating multi-way data can be further improved by an alternating algorithm. THOSVD also unifies a wide range of principal component analysis algorithms.To exploit the potential of generalized algorithms using tscalars for approximating images, we use a pixel neighborhood strategy to convert each pixel to a "deeper-order" tscalar. Experiments on publicly available images show that the generalized algorithm over t-scalars, namely THOSVD, compares favorably with its canonical counterparts.

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Section: A Backgroundsmentioning

confidence: 99%

Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra

Liao¹,

Shen²,

Li³

et al. 2022

Preprint

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show abstract

“…In point view of numerical sign, the subtraction of two diagonal symmetric pixels may be positive or negative in (1). Hence, we can obtain the positive and negative DSP units from the N × N block.…”

Section: Illumination Invariant Measure Under the Dsp With The Evementioning

confidence: 99%

“…Face recognition has been a hot research topic for decades due to its wide application prospects [1]- [3]. The illumination variation problem is inevitable in face recognition, even for the deep learning features [4]- [5].…”

Section: Introductionmentioning

confidence: 99%

Diagonal Symmetric Pattern-Based Illumination Invariant Measure for Severe Illumination Variation Face Recognition

et al. 2020

IEEE Access

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The center symmetric pattern (CSP) was widely used in the local binary pattern based facial feature, whereas never used to develop the illumination invariant measure in the literature. This paper proposes a novel diagonal symmetric pattern (DSP) to develop the illumination invariant measure for severe illumination variation face recognition. Firstly, the subtraction of two diagonal symmetric pixels is defined as the DSP unit in the face local region, which may be positive or negative. The DSP model is obtained by combining the positive and negative DSP units in the even × even block region. Then, the DSP model can be used to generate several DSP images based on the 2 × 2 block or the 4 × 4 block by controlling the proportions of positive and negative DSP units, which results in the DSP2 image or the DSP4 image. The single DSP2 or DSP4 image with the arctangent function can develop the DSP2-face or the DSP4-face. Multi DSP2 or DSP4 images employ the extended sparse representation classification (ESRC) as the classifier that can form the DSP2 images based classification (DSP2C) or the DSP4 images based classification (DSP4C). Further, the DSP model is integrated with the pre-trained deep learning (PDL) model to construct the DSP-PDL model. Finally, the experimental results on the Extended Yale B, CMU PIE, AR, and VGGFace2 face databases indicate that the proposed methods are efficient to tackle severe illumination variations. INDEX TERMS Severe illumination variations, diagonal symmetric pattern, center symmetric pattern, single sample face recognition.

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“…Thanks to the structure of quaternion itself, each pixel of the color image can be represented by a pure quaternion to form a quaternion matrix. This representation is fully utilized in color images edge detection [14], color face recognition [15], color image denoising [16,17], color image completion [3,4], and so on.…”

Section: Introductionmentioning

confidence: 99%

Low Rank Quaternion Matrix Recovery via Logarithmic Approximation

Yang,

Miao,

Kou

2021

Preprint

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In color image processing, image completion aims to restore missing entries from the incomplete observation image. Recently, great progress has been made in achieving completion by approximately solving the rank minimization problem. In this paper, we utilize a novel quaternion matrix logarithmic norm to approximate rank under the quaternion matrix framework. From one side, unlike the traditional matrix completion method that handles RGB channels separately, the quaternion-based method is able to avoid destroying the structure of images via putting the color image in a pure quaternion matrix. From the other side, the logarithmic norm induces a more accurate rank surrogate. Based on the logarithmic norm, we take advantage of not only truncated technique but also factorization strategy to achieve image restoration. Both strategies are optimized based on the alternating minimization framework. The experimental results demonstrate that the use of logarithmic surrogates in the quaternion domain is more superior in solving the problem of color images completion.

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From Grayscale to Color: Quaternion Linear Regression for Color Face Recognition

Cited by 22 publications

References 33 publications

Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra

Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra

Diagonal Symmetric Pattern-Based Illumination Invariant Measure for Severe Illumination Variation Face Recognition

Low Rank Quaternion Matrix Recovery via Logarithmic Approximation

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