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

Carl N. Stephan

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 >13.5m) 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., 1m photographic copy-stands). Herein, basic trigonometry is employed to map PD for two same sized 179mm linear lengths - separated anteroposteriorly by 127mm - as a function of subject-to-camera distance (SCD; 0.2-20m). 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 12m, the within-image PD was negligible (<1%). At <2.5m 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 ≤2mm 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 SCDs should be ignored and no single distance at which PD should be considered negligible (even if one image holds >12m SCD).