Abstract 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.

中文翻译：

---

用于模式识别应用的新分数阶勒让德-傅立叶矩

摘要 正交矩使基于计算机的系统能够区分相似的对象。数学家证明，分数阶的正交多项式在表示给定函数的细节方面优于对应的多项式。在这项工作中，为模式识别应用提出了新颖的正交分数阶勒让德-傅立叶矩。定义了这些矩的基函数，并导出了递推关系、正交性和相似变换（旋转和缩放）的基本数学方程。测试提出的新分数阶矩，将它们的性能与现有的正交四元数、多通道和分数阶矩进行比较。发现新的描述符在准确性方面优于现有的描述符，