The application of affine transformations in matching distorted forensic samples with a common origin.

The practice of forensic odontology regularly requires the forensic dental expert to establish a degree of concordance between two objects, one or both of which have undergone minimal degrees of warping, shrinkage and distortion collectively described as deformations. These comparisons can be between the suspect's or victim's dentition and bite marks on inanimate objects/skin, two radiological images, palatal rugae patterns, dental arches, lip prints and other unique scenarios which are presented in forensic odontological cases. This paper will define the mathematical concept of affine transformation as it pertains to forensic matters and explains how it can be applied to a case study involving pattern deformations. Although the deformation of the evidence may be minimal in extent, it creates a measure of uncertainty when expert evidence is given in court cases. Any metric discrepancy caused by deformation of the evidence will necessitate the application of pattern association and negate the use of metric analysis. It has been shown that a pattern association analysis of evidence will not be affected by minimal amounts of deformation. The mathematical limits of these deformations which will significantly affect the comparisons have not yet been determined. In the case study presented the deformations were considered minimal and thus explainable by a pattern association analysis. The mathematical concepts will empower the expert to explain to a court of law how two samples which were not a perfect match, could in fact be deformed equivalents of common origin.