Mathematics aids fingerprint detection.

Police stations all over the country may soon depend on a mathematical entity called wavelets to help them keep tabs on criminals. The FBI plans to use wavelets to improve the efficiency of fingerprint transmission, storage, and retrieval, thereby making print matching faster and more economical.

Mathematicians use wavelet analysis to process images. The procedure first divides an image into its basic constituents. It then pulls out and saves the constituents that define the image and ignores those that don't contribute information essential to the reconstruction of the image. "This method extracts the coherent parts from the garbage," explains M. Victor Wickerhauser, a mathematician at Washington University in St. Louis. Thus wavelets reduce the amount of data needed. Such "data compression" reduces the time and cost of processing.

The FBI encodes fingerprints with about 30 "minutia points," places where the finger's ridges end, split, or merge. Most data-compression techniques introduce distortions that are invisible to the eye but troublesome for a machine trying to match two fingerprints, says Wickerhauser. These techniques tend to add extra edges that can interfere with correct reading of minutiae. Wavelets do not create such distortions.

One type of wavelet procedure, called the Best-basis Algorithm, came out on top when the FBI tested it and two other technologies for transforming fingerprint images into compact data sets. For the test, the FBI asked experts trained in fingerprint matching to compare real and reconstructed prints.

The FBI was then able to simplify the algorithm further. "On a practical basis, it is almost the same quality, but the complexity is lower," says Wickerhauser, who thinks wavelets will prove valuable in many more applications.