The Statistics of Fingerprints

A Matching Algorithm to be used in an Investigation into the Reliability of the Use of Fingerprints for Identification

Bob HastingsUniversity of Western Australia

• Reliable fingerprint based identification is important because of recent court challenges to fingerprint evidence from human experts.

• The huge size of existing fingerprint databases makes it necessary to have some form of automated classification and matching scheme.

Identification Methodology

Fingerprint Based Identification

• Sample, eg latent fingerprint from crime scene• DNA sample

• Data eg. print from a database• DO THEY MATCH?

• Matcher compares 2 samples => Match Score• Score compared with match threshold

Encoding difference

Distribution of the encoding differences between several samples from the same source

Distribution of the encoding differences between samples from different sourcesP

0

False rejectionFalse acceptance

Acceptance/rejection threshold

False Acceptance vs False Rejection

Any biometric identification system exhibits this kind of behaviour. The challenge is to minimise the area of overlap between to 2 curves so that either a match or a non-match can be declared with confidence.

Large Scale Features

These are part of the broad scale ridge flow pattern.

• Cores (or loops)• Deltas • Whorls

Fine Scale Features (“Minutiae”)

• Occur where ridges bifurcate or terminate.

• Traditionally a specified number of matching minutiae between 2 prints has been accepted as evidence that they are from the same finger.

Large Scale Fingerprint Features

Cores

Deltas

Twin Loop patternLeft Loop pattern

Minutiae Types

BIFURCATIONS

TERMINATIONS

The Problem of Distortion

• Fingerprint matching is carried out using the number and position of large and fine scale features.

• Some distortion is always present because a fingertip is not a flat surface

• Distortion is a property of the method of image capture • Distortion is not necessarily linear

This means that 2 prints taken from the same finger will never have the same features in exactly the same locations.

Proposed Matching Methodology

• Extract the location and orientation of the minutiae in the two prints

• Construct a Feature Descriptor for each minutia based on the locations of other minutiae around it

– A feature descriptor is a square array containing a representation of the location of minutiae around the reference point.

– The array is rotated so as to align with the orientation of the reference minutia.

– A Gaussian smoothing filter is applied to provide some spatial tolerance in the location of points when attempting a match.

• Try to match corresponding minutiae between the 2 images by correlation on the feature descriptors.

Database print, minutiae overlaid

Feature descriptor

for indicated minutia

Latent print from same finger, with minutiae overlaid

Feature descriptor for corresponding minutia

Feature Matching• A similarity score is calculated for each pair of feature descriptors, one

from each image, giving a matrix of similarity scores

• Select the pair with the highest score, then the remaining pair with the next highest score, etc.– Eg. For two prints containing 30 and 20 feature points respectively,

this gives 20 putative matches.• Some of the above putative matches will be wrong

• The RANSAC algorithm is used to find the spatial mapping (here we choose a homography) that best maps locations of points in one set onto point locations in the other set. Putative matches that are inconsistent with this mapping are rejected.

• A MATCH SCORE will then be computed for the pair of images, using– Positions and orientations of the matched minutiae and other

discernible features– Other properties such as the orientation of the ridges at various

points in the 2 images

Matched pairs of feature descriptors for the pair of prints shown below

• Top row = ten-print

• Bottom row = latent print

• Ranked by similarity score, best at left

Putative minutiae point matches

Point matches after applying RANSAC algorithm