Abstract

Image invariants are those properties of the images of an object that re- main unchanged with changes in camera parameters, illumination etc. In this pa- per, we derive an image invariant for smooth surfaces with mirror-like reflectance. Since, such surfaces do not have an appearance of their own but rather distort the appearance of the surrounding environment, the applicability of geometric in- variants is limited. We show that for such smooth mirror-like surfaces, the image gradients exhibit degeneracy at the surface points that are parabolic. We lever- age this result in order to derive a photometric invariant that is associated with parabolic curvature points. Further, we show that these invariant curves can be effectively extracted from just a few images of the object in uncontrolled, un- calibrated environments without the need for any a priori information about the surface shape. Since these parabolic curves are a geometric property of the sur- face, they can then be used as features for a variety of machine vision tasks. This is especially powerful, since there are very few vision algorithms that can handle such mirror-like surfaces. We show the potential of the proposed invariant using experiments on two related applications - object recognition and pose estimation for smooth mirror surfaces.