Perspective distortion in craniofacial superimposition: Logarithmic decay curves mapped mathematically and by practical experiment

Abstract

The superimposition of a face photograph with that of a skull for identification purposes necessitates the use of comparable photographic parameters between the two image acquisition sessions, so that differences in optics and consequent recording of images does not thwart the morphological analysis. Widely divergent, but published, speculations about the thresholds at which perspective distortion becomes negligible (0.5 to >13.5 m) must be resolved and perspective distortion (PD) relationships quantified across their full range to judge tolerance levels, and the suitability of commonly employed contemporary equipment (e.g., 1 m photographic copy-stands). Herein, basic trigonometry is employed to map PD for two same sized 179 mm linear lengths -separated anteroposteriorly by 127 mm -as a function of subject-to-camera distance (SCD; 0.2 to 20 m). These lengths approximate basic craniofacial heights (e.g., tr-n) and widths (e.g., zy-zy), while the latter approximates facial depth (e.g., n-t). As anticipated, PD decayed in logarithmic and continuous manner with increasing SCD. At SCD of 12 m, the within-image PD was negligible (<1%). At <2.5 m SCD, it exceeded 5% and increased sharply as SCD decreased. Since life size images of skulls and faces are commonly employed for superimposition, a relative 1% perspective distortion difference is recommended as the ceiling standard for craniofacial comparison (translates into a ≤2 mm difference in physiognomical face height). Since superimposition depends on relative comparisons of a photographic pair (not one photograph), there is practically no scenario in superimposition casework where subject-to-camera distances should be ignored and no single distance at which PD should be considered negligible (even if one image holds >12 m subject-to-camera distance).

A geometric morphometric evaluation of the Belanglo ‘Angel’ facial approximation

“…Stephan finds a distortion effect of ~ 5% at distances less than 2.5 m, and confirmed earlier studies that 12 m is required for photographic distortion to be negligible (< 1%) [39].…”

“…The foreshortening and widening of the face may also be due to photographic distortion, which causes the lower face to recede and the upper face to expand when the skull is photographed at distances of less than 2.5 m [38,39]. It also the case that errors in assigning the landmarks onto a 2D image [59] may have contributed to the resulting facial shape, and in particular at the mid-ramus and gonion.…”

Estimating the Skull‐to‐Camera Distance from Facial Photographs for Craniofacial Superimposition

“…(4a) A 179‐mm cube photographed at a distance of 0.7 m. (4b) The same cube photographed with the same camera and lens, but at a camera‐to‐subject distance of 4.0 m. (4c) Superimposition of (4a) and (4b). Panel 4 reproduced from Stephan p. 257.e4 with permission from Elsevier.…”

Estimation and reconstruction of facial creases based on skull crease morphology

“…Superimposition of the face-images and the skull-images indicated that some of the face-images may have camera distortion. Earlier research on perspective distortion 10,39 indicate that distortion is unavoidable among the face-images used in this research as it is possible that many of these face-images had been photographed with lensobject distances that are less than 12 m as facial image photography at greater than 12 m distance is indeed rare 39 . Freeform Modelling Plus allows a perspective view in order to correct for close-up images of the subject but the extent of such correction that Freeform…”