In search of illumination invariants

We consider the problem of determining functions of an image of an object that are insensitive to illumination changes. We first show that for an object with Lambertian reflectance there are no discriminative functions that are invariant to illumination. We do this by showing that given any two images, one can construct a single Lambertian object that can produce both images under two very simple lighting conditions.; However, a local analysis of the differential geometry and photometry of an object reveals strong coupling between the object surface geometry, its viewing direction and image statistics. This result leads us to adopt a probabilistic approach in which we analytically determine a probability distribution for the image gradient as a function of the surface's geometry and reflectance and the object's viewing direction. Our distribution reveals that the direction of the image gradient is insensitive to changes in illumination direction. We verify this empirically.; We show two applications of the illumination insensitivity. We use this distribution to develop an illumination insensitive measure of image comparison and test it on the problem of face recognition. It achieves a recognition error rate as low as 1.4% for near orthogonal lighting. As a second application, we develop a motion tracking algorithm exploiting this illumination insensitive measure. It correctly decouples the change in scene caused by the displacement of the object from that caused by lighting variation whereas the traditional methods assume the image intensity is constant for a fixed point on the object without consideration for rapid lighting variations.; The detection of the occluding contours critically aides image segmentation, a crucial task in computer vision. The aforementioned coupling between the object geometry, viewing direction and the image statistics manifests in a special form at the neighborhood of an occluding contour of a smooth object-fold. The tangent field to the image isobrightness contours align with the fold. We consider a simple model of a fold with a Lambertian surface represented by a quadratic function. The calculation shows that the alignment of the image isobrightness contours with the fold is stable under varying illuminations and this alignment extends to reasonably large neighborhoods of the fold. This result is then confirmed by calculating the mean and variance of the isobrightness contours of the object imaged under varying lighting conditions. The stability of the isobrightness contours in a reasonably large neighbourhood of the fold provides the foundation on which we then construct a filter for detecting the folds using the asymmetry of the isobrightness contours on either side of the occluding contour—alignment on the side of the occluding fold, obliqueness on the side of the occluded surface.