Fractional-order quaternion exponential moments for color images

AbstractInspired 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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Novel Color Orthogonal Moments-Based Image Representation and Recognition

10.21203/rs.3.rs-127190/v1 ◽

2020 ◽

Author(s):

Bing He ◽

Jun Liu ◽

Tengfei Yang ◽

Bin Xiao ◽

Yanguo Peng

Keyword(s):

Fractional Order ◽

Color Image ◽

Laguerre Polynomials ◽

Color Images ◽

Polar Coordinates ◽

Coordinate Space ◽

Geometric Invariant ◽

Global Features ◽

Orthogonal Moments ◽

Image Descriptors

Abstract 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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Robust Color Images Watermarking Using New Fractional-Order Exponent Moments

IEEE Access ◽

10.1109/access.2021.3068211 ◽

2021 ◽

pp. 1-1

Author(s):

Khalid M. Hosny ◽

Mohamed M. Darwish ◽

Mostafa M. Fouda

Keyword(s):

Fractional Order ◽

Color Images

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Accurate Computation of Fractional-Order Exponential Moments

Security and Communication Networks ◽

10.1155/2020/8822126 ◽

2020 ◽

Vol 2020 ◽

pp. 1-16

Author(s):

Shujiang Xu ◽

Qixian Hao ◽

Bin Ma ◽

Chunpeng Wang ◽

Jian Li

Keyword(s):

Numerical Integration ◽

Fractional Order ◽

Numerical Instability ◽

Calculation Methods ◽

Image Description ◽

Accurate Calculation ◽

Orthogonal Moments ◽

Instability Problem ◽

Exponential Moments ◽

Numerical Integration Error

Exponential moments (EMs) are important radial orthogonal moments, which have good image description ability and have less information redundancy compared with other orthogonal moments. Therefore, it has been used in various fields of image processing in recent years. However, EMs can only take integer order, which limits their reconstruction and antinoising attack performances. The promotion of fractional-order exponential moments (FrEMs) effectively alleviates the numerical instability problem of EMs; however, the numerical integration errors generated by the traditional calculation methods of FrEMs still affect the accuracy of FrEMs. Therefore, the Gaussian numerical integration (GNI) is used in this paper to propose an accurate calculation method of FrEMs, which effectively alleviates the numerical integration error. Extensive experiments are carried out in this paper to prove that the GNI method can significantly improve the performance of FrEMs in many aspects.

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