The fingerprint template which corresponds to the phase distributions (PDs) of the 1D discrete fractional sine transforms (DFSTs) with various transforms’ orders for the grayscale distributions in the transverse lines of the original fingerprint image is proposed. In addition the recognition accuracy and the robustness of the proposed fingerprint templates are evaluated statistically. The condition to realize the high accuracy of fingerprint recognition using the proposed templates has been made clear on the basis of the Receiver Operating Characteristic (ROC) curve and the minimum error rate (MER). The smallest value of the MER became 19 10 60 . 1 %. As for the robustness of the proposed templates, it has been evaluated statistically by use of the normalized cross-correlation function (NCF) between the original data and the inverse transformed data of the proposed template under the condition that the transforms’ orders are known by an adversary. As a result, the high security of the proposed templates could be indicated. Individual recognition using the biological information has been recently increasing everywhere, for example, in the automatic logging into a PC, the immigration at the airport, and so on. In particular, the fingerprint recognition system has been widely used because of its high reliability and reasonable price [1]. In general, the enrolled fingerprint images are stored as templates in the database referred in the fingerprint recognition process. The information of the templates should be hidden to keep individual biological information secret. Many methods have been recently proposed, for example, the biometric cryptosystems [2][5], cancellable fingerprint templates [6]-[10], and so on. However, in these methods, since the minutia-based templates are basically used, the recognition accuracy tends to become low in comparison with that of the image-based templates. In order to realize the fingerprint templates with high recognition accuracy and high robustness against attacks, we have proposed a new method for generating templates by use of the intensity distributions of the 1D fractional Fourier transforms (FRTs) [11] of original fingerprint images [12,13]. In our method, the FRTs with different transforms’ orders are applied to the 1D data extracted from the 2D original fingerprint image in a specific direction. However, there might be a possibility that the FRT’s order in each line of the fingerprint image is revealed, because the extent of the intensity FRT is dependent on the FRT’s order. In this paper, to solve this problem, we propose the fingerprint templates generated by the DFSTs, and indicate the accuracy of the fingerprint recognition by use of the proposed templates. Specifically, first, we compare the amplitude distribution (AD) and PD of the discrete FRTs (DFRTs), the discrete fractional cosine transforms (DFCTs) [14] and the DFSTs [14] of the fingerprint image, and decide the most appropriate distribution and transform used in the generation process of the proposed fingerprint templates. Next, we evaluate the recognition accuracy of the generated fingerprint templates from the viewpoints of the ROC curve, which denotes the relationship between the false acceptance rate (FAR) and the false rejection rate (FRR), and the MER, where the FAR and the FRR take the same value [15]. In the analysis, the effects of the misalignment in the recognition process are not considered. Finally, we quantitatively analyze the robustness of the templates. 2. DFRT, DFCT and DFST The FRT [11], which is regarded as the generalization of a conventional Fourier transform (FT), was introduced by Namias to solve the problem of a harmonic oscillator in quantum mechanics in 1980 [16]. The FRT of 1D input data u(x) is defined as [11] ] tan / ) ( exp[ ) ( ) ( 2 2 s x x i x u x u p p p , ] sin / 2 exp[ dx s x ixp (1)
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