  A fundamental problem in computer vision is that of inferring the intrinsic,
3D structure of the world from flat, 2D images of that world. Traditional
methods for recovering scene properties such as shape, reflectance, or
illumination rely on multiple observations of the same scene to overconstrain
the problem. Recovering these same properties from a single image seems almost
impossible in comparison -- there are an infinite number of shapes, paint, and
lights that exactly reproduce a single image. However, certain explanations are
more likely than others: surfaces tend to be smooth, paint tends to be uniform,
and illumination tends to be natural. We therefore pose this problem as one of
statistical inference, and define an optimization problem that searches for the
*most likely* explanation of a single image. Our technique can be viewed as a
superset of several classic computer vision problems (shape-from-shading,
intrinsic images, color constancy, illumination estimation, etc) and
outperforms all previous solutions to those constituent problems.
