Last week I discussed questions surrounding the photo of an accused Iranian spy. At first glance the shadows in the photo seem somewhat odd, but a forensic shadow analysis revealed that the shadows are physically plausible. Here I show how this analysis can be further refined to provide even stronger evidence of this photo’s viability.
In the above photo, the shadow of the telephone pole may seem at a peculiar angle as compared to the man’s shadow. Shown below is the result of a forensic shadow analysis used to determine if these shadows are physically plausible. The cast shadow from the pole, car, and man (red dots) and the attached shadows on the man’s shoulders (white dots), each constrain the projected location of the light source. Because these constraints have a common intersection (the black outlined region), the shadows in this photo are physically consistent.
We know from this analysis that the shadows in this scene are physically possible and that the projection of the light source is somewhere in the outlined black region (the intersection of the shadow constraints). Because this intersection is not a single point (and in fact extends upwards to infinity) it is possible that the shadows are in fact not consistent with a single light source, but arose from two different light sources each of which happen to be contained within the same region. As such, the smaller that we can make the intersection of the constraints the more likely it will be that we will detect inconsistent shadows.
As shown below, by simply adding two more constraints from the shadows on the man’s leg we can significantly reduce the constraint intersection size. This makes it that much less likely that this photo is a fake.
It can be challenging to narrowly constrain the projected light source, in part because the shadow to object correspondence can often be ambigous leading to broad individual constraints. As such, the more shadows that can be specified, the more narrow the viable region of the light source will be. This in turn will make it more likely to detect a forgery.