Lee Harvey Oswald

Ever since the assassination of President Kennedy, numerous theories have circulated claiming that Lee Harvey Oswald, the accused assassin, acted as part of a larger criminal conspiracy. It has been suggested, for example, that incriminating photographs of Oswald were manipulated and hence evidence of a broader plot. I have never been particularly interested in these conspiracy theories. I do, however, like that at least one aspect of the theory was testable – were the shadows in the Oswald backyard photo physically plausible or not?

A portion of the argument for photo tampering goes something like this. Consider the shadow cast from Oswald’s body onto the ground. The orientation and length of the shadow suggest that the sun is to Oswald’s left and relatively low on the horizon. The long straight shadow under Oswald’s nose, however, suggests that the sun is directly above him. These seemingly incongruous shadows have led to speculation that Oswald’s head was pasted into the scene. In fact, Oswald himself claimed that the photo was a fake and had been altered to falsely implicate him.

I thought that there was a chance that the photo was fake because it does seem at first glance that the shadows in this photo are inconsistent with one another. I also know, however, that our visual system can be spectacularly bad at judging such things as lighting and shadows in a photo.

In order to reason about the shadows in this scene we need a three dimensional model of the scene (Oswald’s head/body and the ground plane) and the three dimensional location of the sun. In general, determining three dimensional information from a single two dimensional image is an under-determined and difficult problem. Estimating three-dimensional models of a person’s head, however, is relatively easy because of the somewhat constrained and well understood geometry of human heads. 

A frontal and profile view are required to build a 3-D model of a person’s head – Oswald’s mugshots were perfect for this. Once constructued, I was able to estimate the 3-D location of the sun.  A generic articulated 3-D body model was used to model Oswald’s body. With a model of Oswald’s head and body and the location of the sun, I was able to infer the location of the ground plane. Once all of the pieces were put in place, it became clear that all of the shadows were perfectly consistent. Shown below, from left to right, is the backyard photo, my 3-D rendering, an overlay of the shadows, and a magnified view of Oswald’s head showing the well matched shadow under the nose. 

See this paper for more details and a followup paper which addressed other claims of tampering including the shape of Oswald’s chin, the length of the rifle, and his seemingly awkward body pose.

The ability to construct three-dimensional models from a single image is incredibly powerful because it allows us to, among other things, reason about the lighting and shadows in a scene. I predict that the next generation of forensic tools will be increasingly more sophisticated in their ability to construct and reason about the full 3-D scene thus greatly expanding our forensic analyses.

Comments

[george]

So? Is it a composite photo or not? The shadow under his nose (known photographically as "Hollywood glamor lighting" OR ''butterfly lighting" still seems to me to indicate a higher postioned sun as the body shadow on the ground indicates a lower positioned sun.

[ It is not a composite. Although the shadows look peculiar, they are perfectly consistent with the sun located in a single position. Part of what makes the shadow on his face so long is that Oswald is tilting his head forward slightly and he has a relatively large nose. --Hany ]

[george]

Hany: I'm still not convinced. The directional shadow falling off of his nose onto his upper lip is not falling diagonally to the left. The directional shadow falling off his chin onto his neck is, however, falling in that direction.

[It is not the case that cast shadows will necessarily have the same orientation. The shape of the object casting the shadow, the shape of the surface onto which the shadow is being cast, and the location of the camera relative to the shadows, each contribute to the final appearance of the shadows. Many previous studies have shown that our visual system can be quite poor at judging the consistency of shadows because we do not correctly take into account the underlying 3-D structure of the scene. You may think that the shadows look odd, however, I have shown that the shadows in this image are consistent with the 3-D geometry of Oswald's head and a 3-D model of the sun -- the physics and geometry don't lie. -Hany]

[Byron]

Finally. I've been thinking along these lines for years concerning the supposedly inconsistent shadows. It's good to see someone actually went through a legitimate process to explain the difference between the shadows on the face and the shadows on the ground. My guess is that pretty much everyone in the U.S.A. has several family photos in their possession that show "inconsistent" shadows like this.