3-D Stereo Using Photometric Ratios

We present a novel robust methodology for corresponding a dense set of points on an object surface from photometric values, for 3-D stereo computation of depth. We use two stereo pairs of images, each pair taken of exactly the same scene but under different illumination. By respectively dividing the left images and the right images of these pairs, a stereo pair of photometric ratio images is produced. We formally show that for diffuse reflection the photometric ratio is invariant to camera characteristics, surface albedo, and viewpoint. Therefore the same photometric ratio in both images of a stereo pair implies the same equivalence class of geometric physical constraints. We derive a shape-from-stereo methodology applicable to perspective views and not requiring precise knowledge of illumination conditions. This method is particularly applicable to smooth featureless surfaces. Experimental results of our technique on smooth objects of known ground truth shape are accurate to within 1% depth accuracy.