Quaternion fractional-order weighted generalized Laguerre–Fourier moments and moment invariants for color image analysis

Abstract

Orthogonal moments based on Laguerre polynomials, especially the quaternion representation of fractional-order orthogonal moments have attracted interest in the imaging field. However, most of the existing quaternion fractional-order color orthogonal moments (QFr-COMs) based on Laguerre polynomials are constructed on Cartesian coordinate space and do not have direct rotation geometric invariance. Inspired by the idea of polynomial transformation, we present a weighted radial normalized fractional-order generalized Laguerre polynomials (WRNFr-GLPs) in polar coordinate space. On the basis, a new set of quaternion fractional-order weighted generalized Laguerre–Fourier moments (QFr-WGLFMs) is proposed and a fast and reliable computing method for geometric invariance of QFr-WGLFMs also is introduced in this paper. Theoretical analyses and experimental results showed that the proposed QFr-WGLFMs and moment invariants offer enhanced image reconstruction and pattern recognition compared with the existing quaternion fractional-order-based orthogonal moments and deep learning-based​ methods, especially under the conditions of image processing with noise and smooth filtering.