Abstract. This study proposes a new set of moment functions for describing gray-level and color images based on the associated Laguerre polynomials, which are orthogonal over the whole right-half plane. Moreover, the mathematical frameworks of radial associated Laguerre moments (RALMs) and associated rotation invariants are introduced. The proposed radial Laguerre
invariants retain the basic form of disc-based moments, such as Zernike
moments (ZMs), pseudo-Zernike moments (PZMs), Fourier-Mellin moments
(OFMMs), and so on. Therefore, the rotation invariants of RALMs can be easily
obtained. In addition, the study extends the proposed moments and invariants
defined in a gray-level image to a color image using the algebra of quaternion to
avoid losing some significant color information. Finally, the paper verifies the
feature description capacities of the proposed moment function in terms of image reconstruction and invariant pattern recognition accuracy. Experimental results confirmed that the associated Laguerre moments (ALMs) perform better than orthogonal OFMMs in both noise-free and noisy conditions.