Quaternion weighted spherical Bessel-Fourier moment and its invariant for color image reconstruction and object recognition

Yang, Tengfei; Ma, Jianfeng; Miao, Yinbin; Wang, Xuan; Xiao, Bin; He, Bing; Meng, Qian

doi:10.1016/j.ins.2019.07.089

Cited by 25 publications

(11 citation statements)

References 40 publications

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“…The concept of orthogonal image moments was first discussed in the early 1980s, and they can be separated into Cartesian and circularly orthogonal moments. Circularly orthogonal moments, including Zernike moments [8], Bessel-Fourier moments [9], and Legendre-Fourier moments [10], are rotationally invariant and hence the focus of research. However, traditional orthogonal moments have limitations, as their orders can only be integers, reducing their description and anti-noise capabilities.…”

Section: Related Workmentioning

confidence: 99%

Robust Image Watermarking With Quaternion Fractional-Order Polar Harmonic-Fourier Moments Based On Wavelet Transformation: Resistance Against Rotation Attacks

Jing

Ang

Palaniappan

et al. 2023

JIWE

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This study presents a zero-watermarking algorithm that can resist rotation attacks. The algorithm uses quaternion fractional-order polar harmonic-Fourier moments (QFr-PHFMs) based on wavelet-transformation. First, the wavelet-transformation is applied to each component of the host image, which is in RGB three-channel color. The low-frequency sub-bands of each component are then extracted and represented using quaternion algebra. Multiple QFr-PHFMs are calculated, and the invariants of the QFr-PHFMs are utilized to establish the watermark system. The watermark extraction process is also simplified. The detection of the image requires a two-level wavelet transformation, followed by the calculation of multiple invariant moments of the low-frequency sub-image. The experimental results are shown and compared with similar methods. Simulations show that this method can produce high-quality visual effects and withstand noise, filtering, JPEG compression, and cropping attacks.

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Section: Related Workmentioning

confidence: 99%

Robust Image Watermarking With Quaternion Fractional-Order Polar Harmonic-Fourier Moments Based On Wavelet Transformation: Resistance Against Rotation Attacks

Jing

Ang

Palaniappan

et al. 2023

JIWE

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show abstract

“…5) Recent Advance of Definition Extension: Quaternion extension has become a very common strategy in moment-based color image processing [139,[168][169][170][171][172]. In addition, quaternion theory is increasingly used in related fields, including both hand-crafted [173][174][175] and learning-based representation [176][177][178][179].…”

Section: Definition Extensionmentioning

confidence: 99%

A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation

Qi,

Zhang,

Wang

et al. 2021

Preprint

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Image representation is an important topic in computer vision and pattern recognition. It plays a fundamental role in a range of applications towards understanding visual contents. Moment-based image representation has been reported to be effective in satisfying the core conditions of semantic description due to its beneficial mathematical properties, especially geometric invariance and independence. This paper presents a comprehensive survey of the orthogonal moments for image representation, covering recent advances in fast/accurate calculation, robustness/invariance optimization, and definition extension. We also create a software package for a variety of widely-used orthogonal moments and evaluate such methods in a same base. The presented theory analysis, software implementation, and evaluation results can support the community, particularly in developing novel techniques and promoting realworld applications.

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“…The quaternion is a four-dimensional complex number, also known as a hypercomplex. It is composed of one real component and three imaginary part components, and is formally defined in [5]:…”

Section: Representation Quaternion Algebra and Fractional-order Imagementioning

confidence: 99%

“…This experiment was performed on two sets of public color-image databases: (128 × 128)sized color images selected from COIL-100 ( Fig. 9), and (128 × 128)-sized butterfly color images selected from [5] (Fig. 10).…”

Section: Geometric-invariant Recognition In Color Imagesmentioning

confidence: 99%

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Novel Color Orthogonal Moments-Based Image Representation and Recognition

He¹,

Li²,

Yang³

et al. 2020

Preprint

Self Cite

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Inspired by quaternion algebra and the idea of fractional-order transformation, we propose a new set of quaternion fractional-order generalized Laguerre orthogonal moments (QFr-GLMs) based on fractional-order generalized Laguerre polynomials. Firstly, the proposed QFr-GLMs are directly constructed in Cartesian coordinate space, avoiding the need for conversion between Cartesian and polar coordinates; therefore, they are better image descriptors than circularly orthogonal moments constructed in polar coordinates. Moreover, unlike the latest Zernike moments based on quaternion and fractional-order transformations, which extract only the global features from color images, our proposed QFr-GLMs can extract both the global and local color features. This paper also derives a new set of invariant color-image descriptors by QFr-GLMs, enabling geometric-invariant pattern recognition in color images. Finally, the performances of our proposed QFr-GLMs and moment invariants were evaluated in simulation experiments of correlated color images. Both theoretical analysis and experimental results demonstrate the value of the proposed QFr-GLMs and their geometric invariants in the representation and recognition of color images.

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Quaternion weighted spherical Bessel-Fourier moment and its invariant for color image reconstruction and object recognition

Cited by 25 publications

References 40 publications

Robust Image Watermarking With Quaternion Fractional-Order Polar Harmonic-Fourier Moments Based On Wavelet Transformation: Resistance Against Rotation Attacks

Robust Image Watermarking With Quaternion Fractional-Order Polar Harmonic-Fourier Moments Based On Wavelet Transformation: Resistance Against Rotation Attacks

A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation

Novel Color Orthogonal Moments-Based Image Representation and Recognition

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