CSI: the maths of rare fingerprints

Extend your fingers with the palm of your hand facing up and look at your fingertips. You will see curved ridges forming unique patterns. Some of your fingertips may have a whorl or a spiral in the central area while others may, instead, have a place where a ridge bends more tightly than everywhere else. A method to mathematically evaluate the rarity of fingerprints, proposed by Chang Su and Sargur Srihari at the University of Buffalo in the US, starts precisely by identifying this ‘central point’.

When you touch a surface such as glass or plastic, the natural body sweat that adheres to the ridges of your fingertips leaves an imprint. This fingerprint (called latent if left by chance or accident) is a unique mark you leave behind. Even if only part of the ridges of your fingertips are present in this mark, their curvature and orientation can be used to locate the central point, and in turn identify the area of your fingertip that left the partial imprint.

Look at your fingertips again, focusing on the peculiar details this time. You might notice that some of the ridges end abruptly while others divide in two. These details or ‘minutiae’ are the major features of a fingerprint — those used by automatic fingerprint matching mechanisms to identify finger imprints.

But how rare are the minutiae of a fingerprint?

This is a question forensic scientists would like to see answered. A 35cm footprint left at a crime scene is more valuable evidence than a 25cm footprint because a 25cm foot is more common. The large footprint can be useful to drastically reduce the number of suspects while the average-sized one is of less use in identifying the culprit. Similarly, if a certain set of fingerprint features is rare, a partial mark showing those features left at the scene of a crime is valuable evidence.

Su’s and Srihari’s method is the first attempt to help forensic analysts in this regard. After computing the position of the central point of a latent fingerprint, the method identifies minutiae by their location and orientation (the direction of the ridge at the location) with respect to the center. The fingerprint itself is represented by the set of details arranged in a particular way: a unique series of minutiae.

The rarity of a fingerprint can be evaluated by comparing thousands of these series of minutiae using a database of real-life latent fingerprints. The rarity measure is the probability that a particular print shares a certain number of minutiae with a fingerprint chosen at random from the database. If the minutiae of the particular print have unusual locations or orientations, the probability is low indicating a rare fingerprint.

If you look at your fingertips and compare the various features in each of them, you may notice that some details show up in all of them while others are less common. Similarly, forensic scientists today look at hundreds of fingerprints to intuitively understand how rare a particular set of features is.

Su’s and Srihari’s method should make their job easier.


Fingerprint matching in the 1930s. (Photo by Fox Photos/Getty Images)

2 thoughts on “CSI: the maths of rare fingerprints

  1. Céline Miani

    This post is dangerous: I’m gonna spend the wholel day watching my fingertips and assessing the rarity of some of my minutiae. Good job Barbara!


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