Fingerprints Go Digital

1278 NOTICES OF THE AMS VOLUME 42, NUMBER 11 T he new mathematical field of wavelet transforms has achieved a major success, specifically, the Federal Bureau of Investigation’s decision to adopt a wavelet-based image coding algorithm as the national standard for digitized fingerprint records [11, 4, 3]. The FBI standard, which uses an approach known as wavelet transform/scalar quantization (WSQ) image coding, was developed by project leader Tom Hopper of the FBI’s Criminal Justice Information Services Division and Jonathan Bradley and Chris Brislawn from the Computer Research and Applications Group at Los Alamos National Laboratory. The standard, which is entirely within the public domain, involves a 2-dimensional discrete wavelet transform (DWT), uniform scalar quantization (a process that truncates, or “quantizes”, the precision of the floating-point DWT output), and Huffman entropy coding (i.e., encoding the quantized DWT output with a minimal number of bits). The FBI has a database consisting of some 200 million fingerprint records, stored (as they have been since the turn of the century) in the form of inked impressions on paper cards. As part of a modernization program, the FBI is digitizing these records as 8-bit grayscale images, with a spatial resolution of 500 dots per inch. This results in some 10 megabytes per card, making the current archive about 2,000 terabytes in size. (Note that a 3.5” high-density floppy disk holds “only” 1.5 megabytes.) Moreover, the FBI receives on the order of 30,000 new cards (≡ 300 gigabytes) per day, from all over the country, for background checks. After considering these numbers, the FBI decided that some form of data compression would be necessary and undertook a survey of the available image compression technology. Transform-domain data compression is based on finding a signal representation, preferably one computable via a fast transform algorithm, that provides the ability to represent complicated signals accurately with a relatively small number of bits. This role has traditionally been filled by the Fast Fourier Transform and its related fast trigonometric transforms, particularly the discrete cosine transform [22]. Wavelets provide an important class of alternatives, however, whose properties make them particularly well suited for encoding high-resolution imagery, so let’s briefly review the mathematical ideas behind wavelet transforms.