Image analysis by fractional-order orthogonal moments

Orthogonal moments play an important role in image analysis and other similar applications. However, existing orthogonal moments are restricted to integer order, and little investigation of non-integer order orthogonal moments has been conducted to date. In this paper, a general framework of real-order orthogonal moments, also known as fractional-order orthogonal moments, is proposed. In this general framework, fractional-order orthogonal moments can be defined in Cartesian and polar coordinate systems. Shifted Legendre polynomials are implemented in this paper to investigate the properties of fractional-order orthogonal moments. A series of experiments are performed, which demonstrate that fractional-order orthogonal moments are not only capable of region-of-interest (ROI) feature extraction but also have potential for image reconstruction and face recognition and have high noise robustness in invariant image recognition.