When is the shape of a scene unique given its light-field: a fundamental theorem of 3D vision?

The complete set of measurements that could ever be used by a passive 3D vision algorithm is the plenoptic function or light-field. We give a concise characterization of when the light-field of a Lambertian scene uniquely determines its shape and, conversely, when the shape is inherently ambiguous. In particular, we show that stereo computed from the light-field is ambiguous if and only if the scene is radiating light of a constant intensity (and color, etc.) over an extended region.