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Advances in Fingerprint Technology.pdf

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appreciated that the number of trials def<strong>in</strong>ed by the suspect population is<br />

the relevant quantity.<br />

Traur<strong>in</strong>g Model (1963)<br />

Description of the Traur<strong>in</strong>g Model<br />

Traur<strong>in</strong>g19 estimated the chances of co<strong>in</strong>cidental f<strong>in</strong>gerpr<strong>in</strong>t association <strong>in</strong><br />

connection with a proposed automatic identification system. The system is<br />

based on prior selection of reference m<strong>in</strong>utiae on a f<strong>in</strong>ger and the record<strong>in</strong>g<br />

of a number of test m<strong>in</strong>utiae. Relative coord<strong>in</strong>ates derived from the reference<br />

m<strong>in</strong>utiae are used to describe the positions of the test m<strong>in</strong>utiae. As proposed,<br />

the test m<strong>in</strong>utiae appear with<strong>in</strong> the triangular region described by the reference<br />

m<strong>in</strong>utiae, and the approximate positions of the reference m<strong>in</strong>utiae on<br />

the f<strong>in</strong>ger are known.<br />

Traur<strong>in</strong>g made the follow<strong>in</strong>g assumptions:<br />

• M<strong>in</strong>utiae are distributed randomly.<br />

• There are two m<strong>in</strong>utia types: forks and end<strong>in</strong>g ridges.<br />

• The two m<strong>in</strong>utia types are equally likely to occur.<br />

• The two possible orientations of m<strong>in</strong>utiae are equally likely to occur.<br />

• M<strong>in</strong>utia type, orientation, and position are <strong>in</strong>dependent variables.<br />

• For repeated registration of one <strong>in</strong>dividual’s f<strong>in</strong>ger, the uncerta<strong>in</strong>ty <strong>in</strong><br />

the position of the test m<strong>in</strong>utiae relative to the reference m<strong>in</strong>utiae does<br />

not exceed 1.5 ridge <strong>in</strong>tervals.<br />

Under these assumptions, the correspondence of a test m<strong>in</strong>utia requires<br />

its presence with<strong>in</strong> a circular region of radius 1.5 ridge <strong>in</strong>tervals (area = 7.07<br />

square ridge <strong>in</strong>tervals). The chance of a m<strong>in</strong>utia appear<strong>in</strong>g <strong>in</strong> this region is<br />

equal to the m<strong>in</strong>utia density (s) multiplied by the area. The m<strong>in</strong>utia may be<br />

one of two equally likely types, and has one of two equally likely orientations.<br />

The probability of a correspond<strong>in</strong>g test m<strong>in</strong>utia, given acceptable reference<br />

m<strong>in</strong>utiae, P(TM/RM), is therefore given by Equation (9.33).<br />

P(TM/RM) = (0.707)/(4s) = 0.07(s) (9.33)<br />

If the chance of encounter<strong>in</strong>g an acceptable set of reference m<strong>in</strong>utiae on<br />

one f<strong>in</strong>ger is r, then each person has a (10 × r) probability that the reference<br />

m<strong>in</strong>utiae will be present on one of their ten f<strong>in</strong>gers. If the number of test<br />

m<strong>in</strong>utiae is N, then the chance of random correspondence of any one of an<br />

<strong>in</strong>dividual’s f<strong>in</strong>gers with a previously def<strong>in</strong>ed f<strong>in</strong>gerpr<strong>in</strong>t is given by<br />

Equation (9.34).

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