Abstract Here, a new set of fractional‐order moments, named fractional‐order generalized Laguerre moments (FGLM), is introduced. These proposed moments are defined on the Cartesian coordinate system and their basis functions are represented by the fractional‐order generalized Laguerre polynomials. Contrary to the classical Chebyshev, Legendre and Gegenbauer moments, which provide only global feature, our proposed FGLM have the ability to extract both global and local features. Moreover, a new set of rotation, scale and translation invariants of the FGLM, is derived and introduced for image classification and invariant pattern recognition. Just as important, we have presented a systematic parameter selection method for finding the optimal fractional parameter values with respect to pattern recognition applications. Finally, several recursive methods for reducing the computation time of our proposed invariants are also provided in this study. Therefore, to demonstrate the performance of the introduced fractional‐order moments and moment invariants, a number of experimental analysis are performed in terms of global and local features extraction, robustness to noise, invariance to geometric deformations, object recognition and computational speed. The presented theoretical and experimental results clearly show that the proposed fractional‐order moments and their corresponding invariants could be extremely useful in the field of image analysis.

Three-Dimensional Hahn moments are performant tool in the domain of image processing applications and pattern classification. In this work, we propose a new method for computing the Three-Dimensional Hahn moments. This method is based on matrix multiplication and symmetry property to decrease the complexity and computational time for volumetric image reconstruction. Experimental results showed that the proposed method is very efficient in terms of computation time, but also in terms of volumetric image reconstruction capability.