By some counts a surprising number of people believe that the 1969 moon landing was a hoax. These dis-believers point to, among other things, purported inconsistencies in some of the moon landing photos. I’ll describe the application of a new forensic technique that refutes some of these claims.
Shown below is the iconic photo of Buzz Aldrin in which the physical plausibility of the lighting and shadows has been called into question.
I have previously described how cast shadows in an image can be analyzed to determine if they are consistent with a single light source. In order to determine if shadows are authentic, we connect points on a shadow to their corresponding points on the object. These lines should all intersect at a single point (or in the special case, be parallel) — this point is the location of the light source projected into the image. The application of this forensic technique (as shown here) requires a clearly defined shadow to object pairing (e.g., the tip of a cone). Such shadows in the above photo are in short supply thus limiting the application of this forensic technique.
In collaboration with Dr. Eric Kee (Columbia University) and Prof. James O’Brien (UC Berkeley) we recently developed a new forensic technique that can be applied to ambiguously defined shadows . In this analysis, we start at any point on a shadow and draw a wedge-shaped constraint that encompasses all parts of an object to which the shadow may correspond. Shown below is one such constraint. The constraint encompasses the entire sphere because there is no systematic way of reasoning about which part of the sphere is associated with a particular spot on the shadow.
In the above figure, the shaded red region constrains the projected location of the light source. While obviously not as specific as a single line constraint, this approach allows us to analyze all cast shadows in an image.
Because we can now handle ambiguous shadow-object pairings, we can also exploit attached shadows to determine the location of the light source. An attached shadow occurs when an object occludes the light from itself (e.g., a non-full Moon). Shown below, for example, is an attached shadow on the sphere’s surface. The line that is tangent to an attached shadow constrains the projected location of the light source to be on the illuminated side of the object.
Multiple cast and attached shadow constraints can be specified in an image. If the shadows are physically correct, then all of the constraints will share a common intersection (this consistency check is automatically determined using standard linear programming). Any violations of these constraints is evidence of photo tampering.
Shown below is the result of this new shadow analysis applied to the moon landing image. The cast shadow constraints are shown with solid red lines and the attached shadow constraints are shown with dashed lines. All of the constraints are consistent (the triangular region outlined in black denotes a common intersection). Despite some claims to the contrary, the lighting in this spectacular photo is physically consistent.
 Eric Kee, James O’Brien and Hany Farid. Exposing Photo Manipulation with Inconsistent Shadows. ACM Transactions on Graphics, 32(4):28:1-12, 2013.
 Eric Kee’s presentation at SIGGRAPH, 2013.