Restoration of Fingerprint Images Using Discrete Version of the Topological Derivative V. Sekar and D. Nedumaran Central Instrumentation and Service Laboratory, University of Madras, Guindy Campus, Chennai – 600 0025, Tamilnadu, INDIA Phone: 91-44-22202768 Fax: 91-44-22352494 Corresponding Authors E-mail: minervasekar@yahoo.com , dnmaran@yahoo.com Abstract- In Biometrics, fingerprint identification requires higher accuracy for getting clear ridge patterns. But, during acquisition the images are degraded due to geometrically warped, blurred, noisy and down sampled images. Several methods have been attempted to restore the original image and topological derivative (TD) is one such technique we have demonstrated in this work. We computed the TD for an appropriate function associated to the image by assigning a diffusion factor k, which indicates the cost endowed to a specific image. To achieve fast computation time over the traditional Continuous Topological Derivative (CTD), discrete topological derivative (DTD) has been implemented in this work. The performance and efficiency of DTD technique are estimated by calculating the PSNR ratio and compared with the classical methods, which indicates that DTD is capable of producing high quality fingerprint images with greater fidelity than the other restoration techniques. Keywords – Fingerprint, Discrete Topological Derivative, Noise, PSNR, Restoration I. INTRODUCTION Fingerprints are the ridge and furrow pattern on the tip of the finger and are used for personal identification of the people [1]. For identification and verification purposes, it is essential to acquire high-quality fingerprint images. Efficient representation of fingerprints information is a critical task, which has to be obtained by structural transforms and fast algorithms. Different types of restoration algorithms have been used as tools to solve problems in image analysis and pattern recognition. But, fingerprint images containing smooth curves as edges, cannot be efficiently preserved by the well-known restoration methods [2] [3] [4]. In this paper, a novel method, Topological Derivative has been attempted to do the fingerprint image restoration. This automated image restoration method is based on the discrete version of the well-established concept of topological derivative [5] [6] [7] [8]. With this approach, image restoration is performed by calculating the diffusion coefficient k as a function of the Topological Derivative associated to a specific cost function. Finally, several image restoration methods are presented to show the computational performance of DTD over other techniques. II. OVERVIEW OF RESTORATION Fingerprint restoration is the ability to get a processed image from the degraded image for the purpose of getting pertinent information [9]. Over the past three decades, several techniques have been developed, to enhance the quality of the image and to reconstruct the degraded image perfectly. It needs additive degradation modeling and inverse filtering solution. Basically the restoration techniques are based on both spatial and frequency domain. In spatial domain, adaptive spatial filtering is one of the best techniques to restore the heterogeneous pixel characteristics perfectly. Wiener Constrained Least squares, Lucy Richardson and Blind Deconvolution methods are used in frequency domain filtering. Normally deconvolution model is applied on degraded image but determination of correct degradation model is very difficult. To circumvent this problem, priori constraints was introduced by S. Geman et al [10] using Markov random field (MRF) framework with good estimation of acceptable images and optimized solution. Further, the regularization is achieved through restoration process based a priori term [11]. K. Knešaurek and J. Machac [12] implemented Fourier wavelet deconvolution restoration technique in PET images using Butterworth filter and Daubechies wavelet function, which results in 25% increase in the contrast ratio of lungs with 2% increase in noise of the restored image. An integrated framework for simultaneous semi-blind restoration via Mumford–Shah Regularization achieved better level of restoration with segmentation [13]. Blind image restoration (BIR) with wavelet analysis [14] has solved the unexpected restoration due to heavily degraded image and the Point Spread Function (PSF), but the BIR to solve the above problem needs complex wavelet analysis. Topmoki Hiramatsu et al., [15] proposed the Kalman filter method for the automatic and accurate restoration of in-vehicle camera foggy images. A consistent development in computer technology leads to nontraditional treatments to the classic problems of image restoration, which results in more complicated and computationally intensive algorithms. Michael Elad and Arie Feuer [16] developed a supersolution image restoration technique using the maximum likelihood 2009 Third UKSim European Symposium on Computer Modeling and Simulation 978-0-7695-3886-0/09 $26.00 © 2009 IEEE DOI 10.1109/EMS.2009.70 223 2009 Third UKSim European Symposium on Computer Modeling and Simulation 978-0-7695-3886-0/09 $26.00 © 2009 IEEE DOI 10.1109/EMS.2009.70 225 2009 Third UKSim European Symposium on Computer Modeling and Simulation 978-0-7695-3886-0/09 $26.00 © 2009 IEEE DOI 10.1109/EMS.2009.70 225