Obtaining confidence intervals and Likelihood Ratios for body height estimations in images

In forensic practice, height estimations on perpetrators visible in video footage from surveillance cameras are regularly requested. There are several ways to do this. Insight is gained into the difference between actual and measured heights by taking validation measurements of a number of test persons. Variation between actual and measured heights is decomposed into a systematic part (because of height loss by pose, 3D modeling of the scene of crime, operator biases) and a random part (due to natural variation). On this basis a method is described for obtaining confidence intervals for the height, including head- and footwear, of questioned persons in images. Since the number of test persons is usually limited, the result is in terms of the Student's t distribution. In addition, for cases in which a suspect is available, an expression is obtained for the Likelihood Ratio (LR), measuring the strength of evidence of resemblance of actual height of the suspect and measured height of the perpetrator. The Likelihood Ratio depends both on the rarity of the estimated perpetrator's height and its closeness to the suspect's height. Technical theorems included may be relevant for other forensic areas as well.