Dimensional Distortion in the Reproduction of Fingerprint Detail

Dimensional Distortion in the Reproduction of Fingerprint Detail
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     In a June 2002 Washington federal court Daubert hearing, the defense objected to the fact that fingerprint identification is mostly performed from two dimensional representations (impressions) of three dimensional fingers. It was also raised that the three-dimensional aspect has not been tested. The Lockheed Martin 50k x 50k test used two dimensional impressions of inked fingers that did not include a third dimensional element.

     With two-dimensional maps of the earth, the longitudinal lines are often stretched in an effort to keep an equal grid of latitude and longitude relationships. These maps are called equirectangular projection maps. This type of map simply plots polar coordinates of a curved sphere into rectangular x and y axis using a fixed width. In reality, this is not a true reproduction of the information contained in the original source since the earth’s longitudinal lines converge at the poles. "Not all properties can be preserved because the geometry of a sphere is different from that of the plane."(1)

     A Mercator projection map is a different type of map that allows angles on the map to equal compass bearings on the sphere.  A Mercator map has a grid that varies in dimensions to compensate for the distortion created by the conversion of three-dimensional coordinates into two-dimensional map coordinates.(1)  With a Mercator map the relative distances of various coordinates are not accurate. 

     Fingerprint identification is concerned with the same type of conversion difficulties.  A photograph of friction skin on a finger compared with an inked impression of the same finger, whether plain or rolled, will yield different information regarding the spatial coordinates of each characteristic.  Furthermore, a normal rolled fingerprint cannot capture all of the characteristics of a fingerprint in a single roll. Attempts to duplicate large areas of friction skin onto a two-dimensional medium result in a low-quality reproduction of the friction skin detail.  Recorded latent print impressions on three dimensional and flexible substrates generally adds even more distortion regardless of the size of the area reproduced.  One of the most extreme examples is the difference in size of fingerprints in infants compared to the same persons as an adult.  The relative distance in the spatial coordinates of the friction skin characteristics changes as the person grows. The dimensional distortion and relative size of an infant fingerprint compared to the adult print is considerable. 

     In making two-dimensional exemplar prints that represent all the friction skin on a palm or sole major-case-prints must be made.  Major-case-prints consist of multiple “partial” impressions that record all the characteristic based detail of the three-dimensional friction skin. By using small partial impressions of highly curved friction skin, the dimensional distortion in the reproduction of characteristic coordinates is minimized. This keeps the information within allowable limits that does not affect routine fingerprint identification as the spatial relationships of the characteristics used in the conventional method of fingerprint identification are not changed. However, what this does mean is that the exact value of each characteristic coordinate will not be an exact reproduction.  This results from the unique dynamics of each print reproduction itself.  A small variance in distance does not change the spatial relationships of the characteristics.  A slight difference in the relative distances of each characteristic compared is normal and should be expected.  Dimensional distortion from rolled and plain exemplar impressions of highly curved friction skin, can sometimes have several percent dimensional distortion as compared to the friction skin itself due to the different geometry.  Distances of measured characteristics on print impressions may be different than that of the curved friction skin from which the impression was made. However, slight to moderate dimensional distortion does not negate the validity of fingerprint identification and this has been proven in practical application.  This is an axiom and is not an issue pertaining to the accuracy of fingerprint identification.

     The change of spatial geometry between the three-dimensional finger and the two-dimensional contact area always results in a slight information loss due to the differences in the dimensions.  A perfect conversion is not possible.  This concept is found in all dimensional conversions

Craig A. Coppock 2002

Reference:
(1) Hartle, James B, Gravity: An Introduction To Einstein's General Relativity. 2002 Addison-Wesley, San Francisco, pg. 25