New fractional-order Legendre-Fourier moments for pattern recognition applications

•New fractional-order Legendre-Fourier orthogonal polynomials are derived.•New fractional-order Legendre-Fourier moments are defined.•Direct rotation, scaling and translation invariants are derived.•The proposed moments archive high recognition rates in presence of geometric and noise attacks.•The proposed outperformed the classical integer-order Legendre-Fourier moments.•The proposed moments outperformed all existing orthogonal image moments. Orthogonal moments enable computer-based systems to discriminate between similar objects. Mathematicians proved that the orthogonal polynomials of fractional-orders outperformed their corresponding counterparts in representing the fine details of a given function. In this work, novel orthogonal fractional-order Legendre-Fourier moments are proposed for pattern recognition applications. The basis functions of these moments are defined and the essential mathematical equations for the recurrence relations, orthogonality and the similarity transformations (rotation and scaling) are derived. The proposed new fractional-order moments are tested where their performance is compared with the existing orthogonal quaternion, multi-channel and fractional moments. New descriptors were found to be superior to the existing ones in terms of accuracy, stability, noise resistance, invariance to similarity transformations, recognition rates and computational times.