The Statistics of Fingerprints

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The Statistics of Fingerprints

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

Bob Hastings University of Western Australia
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Identification Methodology
Fingerprint Based Identification

• 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.

• Sample, eg latent fingerprint from crime scene
• DNA sample
• Data eg. print from a database
• DO THEY MATCH?
• Matcher compares 2 samples gt Match Score
• Score compared with match threshold

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False Acceptance vs False Rejection
Distribution of the encoding differences between
several samples from the same source
Distribution of the encoding differences between
samples from different sources
P
Acceptance/rejection threshold
0
Encoding difference
False rejection
False acceptance
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.
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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.

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Large Scale Fingerprint Features

• Cores

• Deltas

Twin Loop pattern
Left Loop pattern
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Minutiae Types
BIFURCATIONS
TERMINATIONS
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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.
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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.

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Database print, minutiae overlaid
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Feature descriptor for indicated minutia
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Latent print from same finger, with minutiae
overlaid
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Feature descriptor for corresponding minutia
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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

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• 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

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Putative minutiae point matches
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Point matches after applying RANSAC algorithm