Mathematics behind Fingerprinting.
                     MATHEMATICS 
BEHIND 
FINGERPRINTING
INTRODUCTION
• Things like height, weight, 
and body shape play into 
recognize people. What you 
might not immediately 
think of when 
distinguishing people is 
fingerprints.
Source: 
www.mathnasium.com
HISTORY
• To start, fingerprinting, 
more officially known as 
dactyloscopy, has been a 
tool that dates all the way 
back to the ancient 
Babylonians, but it’s been 
in use in the US since the 
1858.
Source: 
www.mathnasium.com
Reliable scientific 
data source 
• Until DNA profiling came 
along in the mid 1980s, 
fingerprinting was 
considered the most 
reliable scientific data 
source that could help 
convict people of crimes. In 
the last 15 years, 
fingerprinting has come 
under fire though.
Source: 
www.mathnasium.com
Precise 
Measurement
• There’s been a lot of debate 
about how precise the 
measurement and 
calculations are for 
fingerprinting and in the 
last 10 years there have 
been four different people 
who were once convicted 
on fingerprinting alone who 
have been exonerated 
based on new findings. 
Source: 
www.mathnasium.com
Fingerprint 
Pattern
• Well, fingerprints fall into 
three pattern types: loops, 
whorls and arches and the 
process of analyzing these, 
as well as ridge line 
patterns involves heavy 
calculation.
Source: 
www.mathnasium.com
Mathematics 
behind Fingerprint
• Formula that is used to 
express the probability of 
getting at least n number 
of matches between two 
sets of fingerprints. It’s 
this: P(X ≥ n) = P(Z ≥ 
(n−μ))
Fingerprinting 
Algorithms
• Fingerprinting algorithms 
provide functional relation 
between the signal feature 
and the location through the 
table of samples recorded in 
the training database. 
• The training database is 
nothing but samples of the 
function relating the location 
in space to the observed 
feature in the same location.
Hypothesis 
Testing
• Using this formulation, 
performance limits of 
fingerprinting algorithms 
can be characterized using 
well known results from 
hypothesis testing. The 
framework is applicable for 
a general signal feature 
which makes it suitable for 
variety of scenarios.
Probability 
Distributions
• Kullback-Leibler (KL) 
divergence between 
probability distributions of 
selected feature for 
fingerprinting at two 
different locations is 
suggested as a central 
metric that encapsulates 
both accuracy and latency 
of fingerprinting localization 
algorithms.
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