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Advances in Fingerprint Technology.pdf

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Amy Model (1946–1948)<br />

Description of the Amy Model<br />

Amy18 def<strong>in</strong>ed two general contributions to f<strong>in</strong>gerpr<strong>in</strong>t <strong>in</strong>dividuality: variability<br />

<strong>in</strong> m<strong>in</strong>utia type (his facteur d’alternance) and variability <strong>in</strong> number<br />

and position of m<strong>in</strong>utiae (his facteur topologique).<br />

Variability <strong>in</strong> M<strong>in</strong>utia Type<br />

Amy assumed the same possible m<strong>in</strong>utia types as did both Balthazard and<br />

Roxburgh: m<strong>in</strong>utiae could be either forks or end<strong>in</strong>g ridges and could have<br />

one of two opposite orientations. Us<strong>in</strong>g a database of 100 f<strong>in</strong>gerpr<strong>in</strong>ts, Amy<br />

determ<strong>in</strong>ed that the relative frequencies of forks and end<strong>in</strong>g ridges were 0.40<br />

and 0.60, respectively. He also noted that divergence or convergence of ridges<br />

was very common; and that when this occurs, there is an excess of m<strong>in</strong>utiae<br />

with one orientation. Amy estimated a frequency of 0.75 for m<strong>in</strong>utiae with<br />

one orientation and a frequency of 0.25 for m<strong>in</strong>utiae with the opposite<br />

orientation.<br />

With F1 forks and E1 end<strong>in</strong>g ridges <strong>in</strong> one direction, and F2 forks and<br />

E2 end<strong>in</strong>g ridges <strong>in</strong> the other, Amy calculated the probability of a particular<br />

order<strong>in</strong>g (A1) us<strong>in</strong>g Equation (9.11), which reduces to Equation (9.12):<br />

P(Al) = [(0.75) 0.4] F1 [(0.25) 0.4] F2 [(0.75) 0.6] E1 [(0.25) 0.6] E2 (9.11)<br />

P(Al) = (0.3) FI (0.1) F2 (0.45) E1 (0.l5) E2 (9.12)<br />

Amy po<strong>in</strong>ted out that <strong>in</strong> the general case, one does not know the absolute<br />

orientation of the m<strong>in</strong>utia configuration. Accord<strong>in</strong>gly, a probability with the<br />

reversed orientations must also be considered and made part of the calculation.<br />

Thus, P(A2) is given by Equation (9.13):<br />

P(A2) = (0.3) F2 (0.l) F1 (0.45) E2 (0.l5) E1 (9.13)<br />

The total probability of the order<strong>in</strong>g of the m<strong>in</strong>utia configuration (Amy’s<br />

facteur d’alternance) is given by P(Al) + P(A2), which reduces to<br />

Equation (9.14):<br />

P(A) = (0.1) F1+F2 (0.l5) F1+E2 [3 (F1+E1) + 3 (F2+E2) ] (9.14)<br />

Variation <strong>in</strong> Number and Position of M<strong>in</strong>utiae<br />

Amy next considered the variation <strong>in</strong> number and position of m<strong>in</strong>utiae.<br />

Consider a square patch of ridges, n ridge <strong>in</strong>terval units on a side. Let P(L)

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