Polarization is a property of light you may be familiar with. The glare you see when sun-light reflects off of a car is an example of polarized light. All of the waves (vibrations) of the reflected light are parallel to the reflecting surface. Hopefully this illustration will help explain my point.
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This is why polarized sunglasses help to reduce glare when driving or fishing. Most of the light sources you are familiar with, such as the sun or a light bulb, are unpolarized. In other words the electromagnetic waves that make up the light travel equally and randomly in all directions away from the source. Once those unpolarized light waves hit a surface, the direct reflections (or glare) you see, is polarized. Note: you can only see the glare if you are at the appropriate angle relative to the incident surface. As described above, the glare happens because the waves are all now travelling parallel to the surface. Sunglass manufacturers guess that most of the glare you will see while driving will come from surfaces nearly horizontal, and thus they use a polarization filter that blocks horizontally polarized light. In other words they only let light in that isn’t horizontally polarized. See the illustration below:
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Now back to my point about 3D shape from polarization. Suppose you were able to quantify the polarization of light with a camera, you could determine the normal of the surface that light reflected from. Assuming of course the source of the light was unpolarized (which is actually a pretty good assumption). It turns out you can measure the polarization of light with something very similar to a camera, a polarimeter or polarization camera. These devices replace the Bayer filter in front of the sensor, which is normally there to determine wavelength (color), with a filter(s) that determines polarization. Polarimeters and polarization cameras are increasing in accuracy and popularity. There are now several companies commercializing this technology because it offers the benefit of 3D shape from a single vantage point, without the need for two cameras (stereo vision), or projection (such as structured light, laser, or time of flight 3D scanning). In the future polarization cameras could reach price points similar to a regular digital camera giving users point and shoot 3D scanning capabilities.
Check out the commercially available systems for more information.
Polarization camera
http://www.fluxdata.com/2009/09/30/fluxdata-inc-introduces-3-ccd-polarization-camera/
Photon-x
http://www.photon-x.com/technologies.html
I should point out that polarization cameras, while able to capture the relative 3D shape of objects, cannot accurately capture scale on their own. For scale, polarization cameras still rely on traditional techniques of 3D scanning, such as stereo or structured light. Camera calibrations may one day adequately predict distortions and scaling sufficient to get close range objects scaled to accuracy levels that rival current structured light systems.
Thanks to Paul Foster for helping clarify some of these concepts!