Symmetric Objects are Hardly Ambiguous

Given any two images taken under different illumination conditions, there always exist a physically realizable object which is consistent with both the images even if the lighting in each scene is constrained to be a known point light source at infinity. In this paper, we show that images are much less ambiguous for the class of bilaterally symmetric Lambertian objects. In fact, the set of such objects can be partitioned into equivalence classes such that it is always possible to distinguish between two objects belonging to different equivalence classes using just one image per object. The conditions required for two objects to belong to the same equivalence class are very restrictive, thereby leading to the conclusion that images of symmetric objects are hardly ambiguous. The observation leads to an illumination-invariant matching algorithm to compare images of bilaterally symmetric Lambertian objects. Experiments on real data are performed to show the implications of the theoretical result even when the symmetry and Lambertian assumptions are not strictly satisfied.