In the 1940s Florentino Santamaria Beltran, Chief of the Technical Police Laboratory in Madrid, Spain performed a frequency of occurrence study of ten different types of ridge characteristics per 1000 ridges in 1,000 fingerprints (PDF).

Beltran included compound minutiae in his study, i.e., enclosures, short ridges, etc.  If the ridge feature types used in his study are simplified and broken down into only ending ridges  and bifurcations, then the frequency distributions would be as follows:  392 Bifurcations and 744 Ending Ridges (see breakdown HERE).

The results of the study demonstrate a ratio of the frequency distributions for bifurcations to ending ridges as 392 / 744, or 1:1.89.

The ratio of ending ridges to bifurcations established by Florentino S. Beltran nearly precisely equals the ratio established by the Osterburg study [7] where he found 925 bifurcations and 1734 ending ridges in 39 fingerprints with a ratio of 1:1.87, a difference of less than 1%. 

Santamaria may have been the initial inspiration behind recognizing that a numerical standard was not the best approach in quantifying a fingerprint identification. 

His hypothesis is summed up in this quotation from his paper:

“If the value of each characteristic is different, will it not be equally so for each collection of points?” “And if they are different, then why should we say, ‘You must have ten to twelve points to establish identity,’ taking into account of the individual value as though all points has the same value?”, and “In other words, in the face of all logic the total identification value of ten to twelve ridge endings, bifurcations or convergences (which in addition to being invariable, occur very frequently) is at present considered to be equal to that of a collection of an equal number of characteristics points, one or more of which are very rare. This is a state of affairs which I consider should be corrected.” [12]

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The fact that some ridge characteristics occur less frequently than others, and are therefore are more rare, is fundamental for defining quantitative weights for ridge formations. 

Santamaria’s study confirms the frequency of occurrence ratio for bifurcations to ending ridges established by Osterburg.  It may be stated that the relationship between the frequencies, and subsequent quantitative weights, for the ridge formations most utilized by latent fingerprint examiners to effect individualization has been defined with relative accuracy and independently corroborated.