This project explored one particular aspect of inverse rendering: inverse lighting, or determining the lighting in a photograph when everything else is known (the camera, and the object's shape and reflectance). This turns out to be a linear inverse problem, which we formulated as a linear least squares system by expanding the lighting in a simple basis for functions on the sphere. Some cleverness went into accelerating the regularization computations.
As an application of this technique, we solved for the lighting in images of people's faces and used that information to change the lighting, which is a novel and useful kind of "darkroom" manipulation to be able to do to a portrait after the fact.
The first publication of this work is described in our Color Imaging Conference paper; a more complete description with some later results is in Chapter 3 of my thesis.