I recently stumbled upon a bizarre and seemingly improbable image showing a utility pole in the middle of Highway 251 east of Montreal Canada. I don’t mean a downed utility pole; I mean, an upright and functioning utility pole placed directly in the middle of a highway. At first glance, it seemed likely that this was a photo hoax, particularly since the pole’s shadow appears to either be missing or impossibly small.
Shown below is the image in question and a magnified view of the base of the pole. From the shading on the pole (brighter on the left and darker on the right) it is clear that the sun is to the pole’s left. This suggests that the pole’s shadow should be cast to the right. The shadow on the roadway, however, seems oddly small given the size of the pole.
At first glance I thought that it was possible that the pole was digitally inserted, that the forger forgot to add its shadow, and that the thin black shadow on the road was cast from an overhead cable. Given the simplicity of this scene — a single distant light source, a cylindrical pole, and a planar roadway — it is fairly straightforward to determine if this scene is physically plausible. That is, is there a reasonable 3-D configuration of these scene components that gives rise to the shading and shadows in this image?
Shown below is a 3-D rendering of the basic components of the above scene. In order to generate this image, I created a virtual camera with a 50mm focal length. The camera was placed 60 feet away from the pole and 6 feet above the ground plane. I then adjusted the direction of the light until the orientation of the shadow matched. In order to match the width of the shadow, I rotated the ground plane 4 degrees away from the camera. In the second image below I’ve colored the pole and shadow red and superimposed it atop the original image. In this image you can see that the shadow is a perfect match.
This 3-D reconstruction is not unique — there are any number of 3-D scene and camera configurations that would have led to the same scene. The reason is, in part, that there is an inherent ambiguity between the distance to objects in the scene and the camera focal length. The point, however, is that a reasonable scene and camera configuration can give rise to the shading and shadows in this image. So while the configuration that I chose may not exactly match the real world scene, it does prove that the scene is physically possible.
It is clear from this 3-D reconstruction that the highly compressed shadow is simply a result of perspective foreshortening. That is, the road is slanted slightly away from the camera and this causes a compression in the cast shadow. We saw this same effect in The Case of the Missing RPG Shadow.
In general, I have found that this sort of 3-D rendering can be extremely helpful in the analysis of images (as it was, for example, in my analysis of the Lee Harvey Oswald photo). This is particularly true when making judgments of 3-D geometry that can otherwise be difficult to make from only a single image.