© Jain, 2004
AnthropometryAnthropometry
M. Bertillon conjectured that the measurements of
certain bony portions of the human frame do not vary
during the period between adolescence and extreme
old age. He selected head length, head breadth,
middle finger length, foot length and cubit. He
quantized these measurements into three classes:
small, medium, and large resulting in 243 bins.
Each primary heading is successively subdivided
according to height, span, length and breadth of the
ear, height of the bust, and eye color, this latter
providing 7 divisions. So the total number of bins is
310 x 7
© Jain, 2004
Bertillon SystemBertillon System
The Bertillon system (1882) entailed
photographing the subject looking
directly at the camera, then in profile,
with the camera centered upon the
right ear. Besides the two photographs,
the subject's height was recorded,
together with the length of one foot, an
arm and index finger.
http://www.tld.jcu.edu.au/hist/stats/bert/
© Jain, 2004
Fingerprint ClassificationFingerprint Classification
• Assign fingerprints into one of pre-specified types
Plain Arch Tented Arch Right Loop Left Loop
Plain WhorlAccidental Pocket Whorl Double Loop
© Jain, 2004
Fingerprint ClassificationFingerprint Classification
• Classify fingerprints for binning/indexing
• Goal: 99% classification accuracy with 20% reject
rate
• Even experts cannot always do correct classification
• Natural frequencies of W, L, R and A (A + T) are
27.9%, 33.8%, 31.7% and 6.6%
© Jain, 2004
© Jain, 2004
Classification Using Orientation Field Flow Curves
Estimate
Orientation Field
Generate OFFCsInput Fingerprint
Classify
fingerprint
Isometric maps
and features
A, L, R, or W
© Jain, 2004
Orientation Field Flow Curves
Left loop
• Study the topology of the
curves formed by ridges
• OFFC is a curve inside a
fingerprint image whose
tangent direction is
parallel to the direction
of the orientation field
• Starting points of OFFCs
are chosen along the
vertical and horizontal
lines passing through the
midsection of the image
© Jain, 2004
Orientation Field Flow Curves
© Jain, 2004
Isometric Maps
• Geometric characteristics of OFFCs are captured by the changes
occurring in the tangent space as we traverse along OFFC
1. Let pj = (xj; yj), j = 0, 1, 2, …, N be equidistant points (at a
distance δ) on the OFFC
2. Approximate the tangent vector at pj by the chord vector:
The unit vector is ej = Vpj/||Vpj||. Obtain the isometric
maps in terms of rotation angles γj with cos γj = e0 ● ej,
where ● is the Euclidean inner product on R2
© Jain, 2004
Isometric Maps
© Jain, 2004
Classification Results
• No. of sign-change points, values of the local max/min
between sign-change points are potential features
• NIST 4 database containing 2,000 fingerprint image pairs
• 800 fingerprints from each of the 5 classes: W, L, R, A and T
• Classification accuracy into 4 classes: 94.4%.
True/Assigned A L R W Accuracy (%)
A 797 2 1 0 99.62
T 781 19 0 0 97.62
L 63 730 1 6 91.25
R 75 4 720 1 90.00
W 12 23 18 747 93.34
© Jain, 2004
Classification Errors
Oversmoothing of orientation field: True class: L; Assigned class: A
Detection of spurious loops: True class: A; Assigned class: L