Lambertian surface reconstruction
To 3-d scan a Lambertian surface with a plain video camera and a light:
Move a point source of light near a Lambertian surface as you capture video from a camera stationary relative to the surface. Pixelwise differences between frames show the effect of removing the source from one frame and adding it to another. Hypothetically, ambient diffusion from other reflectors contributes negligibly to this difference, since the source is close to the surface being scanned. Given an estimated depth for each pixel and per-frame estimated light locations in 3-space, you can compute a simulated frame difference, which you can compare to the real frame difference to get an error. Each pixel of this error is a nonlinear (?) function of ten unknowns: the two x, y, z of the light locations, the estimated depth to that pixel, the surface gradient depth at that object point, and the estimated reflectance at that point. Given just one such error image, we can optimize the two light locations to minimize the error using gradient descent, holding the estimated depths fixed, or we can optimize the depths