"There are two possible outcomes: if the result confirms the hypothesis, then you've made a measurement. If the result is contrary to the hypothesis, then you've made a discovery."

Enrico Fermi

A fingerprint "ridge vector" may be defined as the magnitude or "discriminating value" of a ridge feature type that bears direction or aim to its nearest neighbor or “target” minutia (M).  What is important here is not the discriminating value of a particular ridge feature in this case but instead whether or not the angle of rotation (θ) (see Figures 1 and 2), are consistent with normal displacement of ridge features from the same source.

The displacement of minutiae targets between ridge vectors from the same source can be measured in terms of degrees using a protractor.  Displacement is a vector quantity, which refers to how far out of place an object is.  It is the object's overall change in position. 

The ridge vector may be placed on a circular coordinate system or polar x-y axis in which it’s origin, O, is defined by the point perpendicular and parallel to its adjacent ridges. The ridge vector’s direction leads from this point, indicated by the arrow and aims at the target neighbor.  In this circular coordinate system, the target neighbor is represented by the spatial distance “r” from the origin and the angle of rotation (θ) between the x-axis and the line from the origin to the target neighbor (minutiae “M”) (see below Figures 1 and 2). 

Figure 2

Quality of agreement between pairs of ridge features in two impressions should not only consider friction skin elasticity “stretch” and “compression” thresholds, but also “rotational” thresholds. 

In order to define friction ridge skin elasticity rotational thresholds, the difference between ridge vector angles of rotation present in pairs of latent vs. exemplar corresponding ridge features from the same source were examined by performing the following experiments:

Experiment #1

A total of 2057 pairs of corresponding ending/bifurcating ridge formations from 39 randomly selected pairs of photographically enlarged rolled vs. flat fingerprint impressions from ten-print cards were used.  Ridge vector angles of rotation (θ) for each pair of corresponding ridge formations to its nearest neighbor were measured using a protractor to the nearest 10 degrees. 

All of the pairs of angles of rotation, except one, were displaced by less than 10 degrees.  Only 1 pair displayed ridge direction in gross disagreement in which the angles of rotation (θ) for the 2 ridge vectors were displaced by roughly 50 degrees.   This pair of dissimilar corresponding ridge formations was deemed an anomaly and not consistent with normal friction ridge skin elasticity thresholds.
 

Experiment #2

A total of 267 pairs of corresponding ending/bifurcating ridge formations from pairs of latent vs. flat fingerprint impressions were used.  Latent impressions were deposited in a natural, spontaneous manner consistent with normal handling, developed using standard black fingerprint powder, lifted using standard lifting tape, and placed on standard latent lift cards. The substrates used were 81% glass, 9% metal and 9% plastic.  Each substrate was flat, dry, and relatively clean.  Each latent print fingerprint number and substrate combination was different. 

The corresponding ridge features in the latent impressions were compared to those in the flat impressions from the same source.  Each pair of corresponding ridge vector angles of rotation was measured for positional displacement using a protractor to the nearest 10 degrees. 

No pairs of corresponding ending/bifurcating ridge vector angles of rotation displayed displacement greater than 10 degrees.    

Conclusion

Based on the above experiments, ridge vector angles of rotation displacement of 10 degrees served as the threshold for relative rotational agreement between ridge vectors.  As a result, agreement of rotational positions between pairs of corresponding ridge vectors and the nearest neighbor for each was defined as ±10 degrees.

Pairs of latent vs. exemplar ridge vectors with angles of rotation displacement greater than 10 degrees to the nearest neighbor of each were considered out of tolerance and therefore subject to reduction.  The reduction factor applied was set as the same as that for ridge features displaying distal displacement (see Friction Skin Elasticity).

Note:  For purposes of performing routine casework in a timely manner,  professional judgment usually suffices to determine whether, or not, a pair of latent vs exemplar ridge features are out of tolerance in terms of rotational displacement.  As a result, only when spatial relationships in terms of rotational displacement are ambiguous should ridge vector angles of rotation between pairs of latent vs. exemplar ridge features be carefully measured.  In any case, the placement of the polar x-y axis, ridge vector origin (O), its aim or direction to its nearest neighbor target minutia (M), and angle of rotation (θ) displacement, should speak for itself and allow demonstration, even to the layman.

Protractor

"A painstaking course in qualitative and quantitative analysis by John Wing gave me an appreciation of the need for, and beauty of, accurate measurement."

Paul D. Boyer