Whitening for Photometric Comparison of Smooth Surfaces under Varying Illumination

We consider the problem of image comparison in order to match smooth surfaces under varying illumination. In a smooth surface nearby surface normals are highly correlated. We model such surfaces as Gaussian processes and derive the resulting statistical characterization of the corresponding images. Supported by this model, we treat the difference between two images, associated with the same surface and different lighting, as colored Gaussian noise, and use the whitening tool from signal detection theory to construct a measure of difference between such images. This also improves comparisons by accentuating the differences between images of different surfaces. At the same time, we prove that no linear filter, including ours, can produce lighting insensitive image comparisons. While our Gaussian assumption is a simplification, the resulting measure functions well for both synthetic and real smooth objects. Thus we improve upon methods for matching images of smooth objects, while providing insight into the performance of such methods. Much prior work has focused on image comparison methods appropriate for highly curved surfaces. We combine our method with one of these, and demonstrate high performance on rough and smooth objects.