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.
THANK YOU Share presentations online and avoid the hassle of downloading various presentation sharing software. Also, you can share your presentations in both Public and Private ways. Keep sharing your presentations at SharePresentation Website. Website Link: https://www.sharepresentation.com/ Presentation Link: https://www.sharepresentation.com/yashicavashishtha1065/mathematicsfingerprinting-education Follow us on Social Media Platforms: Facebook: https://www.facebook.com/sharepresentation Twitter: https://twitter.com/SharePresent LinkedIn: https://www.linkedin.com/company/share-presentation