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.
Highlights
In the last decade, image moments and geometric invariance of moments have emerged as effective methods of feature extraction from images [1, 2]
4 Conclusions This paper proposed a new set of quaternion fractional-order generalized Laguerre moments (QFr-GLMs) based on Generalized Laguerre polynomials (GLPs) and quaternion algebra
As color-image feature descriptors, the proposed QFr-GLMs can be used for color-image reconstruction and feature extraction, and the image moments are available for global and local color image representations in the field of image analysis
Summary
Image moments and geometric invariance of moments have emerged as effective methods of feature extraction from images [1, 2]. Both methods have made great progress in image-related fields. Most of the existing algorithms extract the image moments only from grayscale images. Color-image processing is traditionally performed by one of the three main methods: (1) select a single channel or component from the color space of a color image, such a channel from a red–green–blue (RGB) image, as a grayscale image and calculate its corresponding image moments; (2) directly gray a color image, and
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