Image Computing: Fractional Spectra and Circular Moments via FrFT

In image computing, feature extraction plays a key part for image pattern classification. In this article we adopt discrete fractional Fourier transform (FrFT) for fractional feature extraction. Firstly, a criterion is proposed to determine the FrFT order for an image class so that it may be optimally discriminated from other classes in the FrFT domain, and the transformed features are called fractional spectra. Secondly, four types of fractional moments respectively called circular center, circular range, circular skewness, and circular kurtosis are defined and computed from the FrFT results of an image with different FrFT orders. The extracted image features are then classified with a previously proposed nonlinear classifier called kernel-based nonlinear representor (KNR). And face recognition experiments are taken for illustrative examples.