Advances in Fingerprint Technology.pdf

Table 9.4 Champod’s Upper Bound Frequencies for Minutia Orientations
in the Three Statistically Different Regions of Fingerprints
Minutia Type Above Delta Opposite Delta Beside Delta
Ridge endings, positive 0.332 0.359 0.190
Ridge endings, negative 0.708 0.690 0.841
Bifurcations, positive 0.439 0.235 0.246
Bifurcations, negative 0.622 0.815 0.809
Other bifurcation types, positive 0.442 0.294 0.264
Other bifurcation types, negative 0.666 0.863 0.821
upper-bound frequencies for each of the minutia types having orientation
were determined for each of the three non-delta quadrants. These frequencies
are presented in Table 9.4.
The frequencies in Table 9.4 did not vary by finger or by ridge count.
Some of the frequencies were pattern dependent, suggesting that orientations
are influenced by the position of deltas. The orientation frequencies were
found to be partially dependent on the type of minutia, but independent of
the number of minutiae present.
Lengths of Compound Minutiae. Lengths of each of the compound minutiae
(other than the bridge and spur) were grouped into five intervals. The
distribution within each of the intervals was determined and these distributions
were compared in different regions of the fingerprints. Again, only the
occurrence of short ridges and dots was found to vary with position on the
print. The length variable for the other compound types was found to show
regional independence. Each of the compound minutiae was independent of
the number of minutiae and their relative orientations.
Conclusion
Champod and Margot found that their data and the statistical analysis confirmed
and refined the validity of a calculation model used to express the
probability of a configuration of minutiae.
Using their conservative, upper-bound estimates, they calculated the
probabilities of occurrence of two minutia configurations under their model.
One of the configurations had seven fundamental minutiae (five ridge endings
and two bifurcations). This configuration was assigned a probability of
1/40,000. The second configuration had three fundamental minutiae and
three combined minutiae (three ridge endings, one enclosure, one spur, and
one opposed bifurcation). This configuration was assigned a probability of
1 in 1.42 × 10 9 . It was noted that these calculations did not take into account
the probability of the ridge arrangements; inclusion of this additional constraint
would make the probability still lower.