Stereoscopic Image Description with Trinion Fractional-Order Continuous Orthogonal Moments

2021 ◽  
pp. 1-1
Author(s):  
Chunpeng Wang ◽  
Bin Ma ◽  
Zhiqiu Xia ◽  
Jian Li ◽  
Qi Li ◽  
...  
Keyword(s):  
Fractional Order ◽  
Stereoscopic Image ◽  
Image Description ◽  
Orthogonal Moments ◽  
Order Continuous

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

scholarly journals Accurate Computation of Fractional-Order Exponential Moments

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.

Generic orthogonal moments: Jacobi–Fourier moments for invariant image description

2007 ◽  
Vol 40 (4) ◽  
pp. 1245-1254 ◽  
Author(s):  
Ziliang Ping ◽  
Haiping Ren ◽  
Jian Zou ◽  
Yunlong Sheng ◽  
Wurigen Bo
Keyword(s):  
Image Description ◽  
Orthogonal Moments

scholarly journals Quaternion fractional-order color orthogonal moment-based image representation and recognition

2021 ◽  
Vol 2021 (1) ◽  
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

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.

scholarly journals On positive normalization of fractional order continuous disturbance singular system

2019 ◽  
pp. 34-38
Author(s):  
Muhafzan ◽  
Admi Nazra ◽  
Lyra Yulianti ◽  
Zulakmal
Keyword(s):  
Linear System ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Closed Loop ◽  
Singular System ◽  
Research Field ◽  
Loop System ◽  
Sufficient Condition ◽  
Closed Loop System ◽  
Order Continuous

Recently, the fractional order continuous singular system becomes research field that much discussed by various researchers. The normalization constitutes a variant of discussing for fractional order singular system. The procedure to normalize positively of the fractional order continuous disturbance singular system is discussed in this paper. Some sufficient condition that guarantees the existence of a fractional derivative output feedback such that the closed loop system constitutes a fractional order usual linear system and positive, is established. The considered problem is solved by transforming it into a usual fractional order linear system, and afterwards it is analyzed using algebraic principle. The final result of this paper is a sufficient condition that guarantees the existence of a fractional derivative feedback such that the closed loop system constitutes a fractional order usual linear system and positive.

scholarly journals Novel Color Orthogonal Moments-Based Image Representation and Recognition

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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