1. Fingerprint Imaging: Wavelet-Based Compression and Matched Filtering Grant Chen, Tod Modisette and Paul Rodriguez ELEC 301 : Rice University, Houston, TX Wavelet Compression Compression Algorithm Matching Algorithm Fingerprint Matching Acknowledgements Results Thanks to Professor Richard Baraniuk for teaching the ELEC 301 class. We would also like to acknowledge previous work done by the following groups which provided inspiration for our project: Wavelet-Based Image Compression No Waldo Here, Just My Bala : Image Matching What are possible methods for image matching? What matching strategy works for fingerprints? How does the program detect a match? Image matching has many applications outside of fingerprinting, therefore, many different methods have been developed. Two images of equal size can be compared pixel by pixel to find differences. The directions and orientations of a print can be converted into a matrix of vectors which are then compared. Also, different characteristic features of one image can be matched to the full image to determine where matches occur. Fingerprints differ from typical photo images because one person’s prints can be obtained at different angles and levels of darkness. This makes matching two images of a person’s fingerprint taken at separate times difficult. Our strategy is to compare small sections of the fingerprint against a whole stored print with the goal of finding several individual feature matches. The small sample of the fingerprint (template) is convolved with the image of a whole fingerprint (reference). This convolution returns a maximum value in the place where the template most resembles the reference image. If this correlation is strong enough, we have a match. Obtain Samples : Template – Part of Image Reference – Whole Image Normalize Template & Reference with L2 Norm Flip Template to Counter the Convolution Flip Find Convolved Array : Convolve Template & Reference Find Energy Norm : - Convolve Array of Ones w/ (Reference) 2 - Take Square Root of Convolution Normalize Convolution Array By Dividing by Energy Norm Take Convolution Array to N th Power (8) to Emphasize Peaks Max Convolution Array -> POINT OF MATCH Wavelet image compression is just one of the many applications of wavelet technology. Wavelets are important because unlike one-dimensional Fourier analysis which is localized only in frequency, wavelet basis are two-dimensional, localized in both frequency and time. One application of wavelet compression is digitally storing and compressing the FBI’s library of fingerprints. Aside from saving a great deal of physical space, this allows for computational analysis of the fingerprints. The goal of this project is to determine if wavelet compressed fingerprints retain enough detail to meet the very precise demands of algorithms which match the individual ridges and swirls of human fingerprints. We employ bi-orthogonal wavelets in order to transform the prints and hard thresholding in order to compress the coefficient values. Many different methods of matching the fingerprints with the compressed versions are tried as well. Obtain fingerprint samples in uncompressed form Digitize the prints in 256 grayscale at 48000 pixels per square inch. Take the 2 dimensional discrete wavelet transform of the image. For this purpose we chose to use biorthogonal wavelets of the Deslauriers-Dubac family because they are the most widely used for image compression. For biorthogonal wavelets the requirement of orthogonality is relaxed in order to construct more compact and symmetric wavelets. Employ hard thresholding. In this lossy compression method a threshold value is selected and all coefficients below this value are rounded to zero. This is the form in which the compressed fingerprint data is stored. When the print is needed again, an inverse discrete wavelet transform is applied to the data and a reconstruction of the original fingerprint is obtained. Matching at 15:1 compression In all cases at 8:1 compression we were able to successfully identify the reconstructed fingerprint. Using dark, clear fingerprint samples we were able to identify key points at compressions up to 15:1, which is the ratio required by the FBI for compression of their own databases. Our choice of using hard thresholding to compress images limited us most in recognizing the features of the reconstructed prints. Throwing out coefficients created uneven losses in different parts of each image. We could improve the compression ratios greatly by replacing the thresholding with a form of scalar quantization of the wavelet coefficients. This lossy compression evenly degrades our image, which is preferential since we need to always have the whole image available so it can be searched. Non-Match