Advances in Fingerprint Technology.pdf

of any occurrences that appear in the cell. The latter were determined from
Osterburg’s data and are presented here in the final column of Table 9.2.
Discussion of the Osterburg Model
The Osterburg model is appealing because it is simple to apply and is statistically
sophisticated. It is particularly useful for the comparison of individuality
among different fingerprints. If some standard configuration of
minutiae is defined, the model provides a means to compare other minutia
configurations to the standard. The feature that allows this comparison is
simply the weighting of compound minutiae by their frequencies of occurrence.
Both Santamaria 44 and Kingston 20 had used this concept, but Osterburg’s
treatment is far more rigorous and perceptive. He has been the only
investigator to consider the errors in minutia frequencies. Santamaria’s
method amounted to a mere suggestion that compound minutiae be
weighted according to the number of fundamental minutiae composing
them. Kingston used actual frequencies of occurrence of the compound
minutiae, but did not consider errors in these frequencies and did not give
his criteria for classification of compound minutiae types. As a result, one
does not know when two closely spaced minutiae should be considered as a
compound form. Osterburg defined his compound minutiae precisely, and
Sclove provided definite treatment for other closely spaced minutiae.
Positioning of minutiae is also well treated for comparing the individuality
of different fingerprints. Osterburg defined position using a millimeter
grid that divided the fingerprint into discrete cells. Discrete cells allowed
extensive treatment of correlation by Sclove, making the model robust to
local variations in density. (Recall that these variations had been a major
problem in Kingston’s model.) Osterburg ignored positioning within the
cells, but the cells were small, equivalent to about two ridges on a side.
Furthermore, Sclove’s treatment of multiple events provided flexibility within
the cell structure.
Cells that are empty contribute to individuality within the Osterburg
model. This is an important feature that has not been included in many of
the fingerprint models. Bose 30 was the only other investigator to directly
consider the value of featureless ridges. Bose’s rudimentary model allowed
four equally likely events at each square ridge interval, one of which was a
continuous ridge. His model grossly exaggerates the value of a continuous
ridge: a single ridge extending for five ridge intervals would be assigned a
frequency of less than 1 in a 1000. It is clear, however, that a patch of ridges
without minutiae does possess some individuality. Cummins and Midlo 48
pointed out that this contribution makes their estimate of fingerprint individuality
more conservative. The other Henry-Balthazard models, 15,16,31,33
along with Roxburgh 17 and Trauring, 19 deny this contribution. Kingston 20