Face Recognition Based On The Statistics Of Fractional Fourier Transform

Face recognition,as an important field of biometric recognition technology, is of great important value in theory and application. It is an intuitive, simple and high stability recognition method. As a generalization of Fourier transform, Fractional Fourier transform(Fr FT) is a new and powerful image processing tool in recent years, which can be seen as performing a rotation of a signal to any angle from the time axis to the frequency axis.The Fr FT with different transform orders contains the time-frequency information of the signal at the same time,which has a broad application prospect in the field of image processing and pattern recognition. In order to solve the robust problem and small sample size problem, it merges the Fr FT and face recognition algorithm, which has a deep learning about the statistical information of Fr FT.The main content of this paper for facial image recognition rests on the following facts:1. Firstly, it introduces the development status of face recognition in several parts, which include the background, research state and the main algorithm in spatial domain and transform domain.Then, it gives a brief introduction about the definition of Fr FT and discrete Fr FT. Based on them,it gives the definition of two dimensional fractional Fourier transform and discrete form.2. Secondly, Fr FT is not reality preserving, since we introduce a new method which makes full use of the amplitude information of the two dimensional discrete fractional Fourier transform(2D-DFr FT) for face recognition.This new method makes use of the amplitude information of different transform orders to verify the discriminant ability of amplitude information,and then merges the different orders’ amplitude information of 2D-DFr FT.In addition,the amplitude information is robust to the map structure, which can solve the problem existing in the locality preserving projection.3. In this paper, a band fusion method based on the fractional Fourier domain for face recognition is proposed. It merges different orders’ generalized phase spectra of two dimensional fractional Fourier transform(2D-Fr FT). In particular, features are extracted from the phase parts of the 2D-Fr FT called generalized phase spectra.The new feature extraction method based on 2D-Fr FT can be decomposed into three steps: division of the 2D-Fr FT’s transform orders, generalized phase spectra extraction of 2D-Fr FT, and generalized phase spectra band fusion. Through selecting the appropriate transform orders and choosing the generalized phase spectrum band with high trace ratio, a new spectrum feature can be extracted, which not only contains the smooth information but also includes the edge information of a facial image.4. Finally, it proposes a method based on the difference in the faces. Unlike the aforementioned work focusing on the original face image recognition, we argue that the difference between images contains more discriminative information than the original images. The difference of an individual’s different images is smaller than the different individuals’ face images. Specially, 2D-DFr FT is put into the image processing and then extracts the phase information in order to make full use of the sparsity of face images. During the experiment, each person extract one image for training, and the rest images are for test. The experiment results not only show the effectiveness of the proposed method, but also solve the small sample size problem.