Touchless Fingerprint Biometrics

Touchless Fingerprint Recognition

 103

the finger curvature along the z-axis. The height z of every row of Z

s

is proportional

to the width of the same row in I

R

.

The polynomial p is imposed to pass through the points (x

min

,0), (x

m

− x

m

·

c

W

, c

H

), (x

m

+ x

m

· c

W

, c

H

), (x

max

,0),wherex

min

is the left limit of I

R

along the

horizontal axis, x

max

is the right limit of I

R

along the horizontal axis, and x

m

=

(x

max

+ x

min

)/2, c

W

and c

H

are values empirically estimated from the analysis of

real three-dimensional fingerprint models.

To obtain a first estimation of the finger height, the polynomial p is fitted in the

interval from x

min

to x

max

, obtaining the vector C.

Then, the height of every row i of Z

s

is computed as follows:

Z

s

(i) = I

R

(i) × C × (X

min

(i) − X

max

(i)), (5.17)

where