language: en

3-D Stereo Using Photometric Ratios

Lawrence B. Wolff Elli Angelopoulou
Computer Vision Laboratory Department of Computer Science The Johns Hopkins University
Baltimore, MD 21218

ABSTRACT 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. The methodology utilizes multiple stereo pairs of images, each stereo pair taken of exactly the same scene but under different illumination. With just 2 stereo pairs of images taken respectively for 2 different illumination conditions, a stereo pair of ratio images can be produced; one for the ratio of left images, and one for the ratio of right images. We demonstrate how the photometric ratios composing these images can be used for accurate correspondence of object points. Object points having the same photometric ratio with respect to 2 different illumination conditions comprise a well-defined equivalence class of physical constraints defined by local surface orientation relative to illumination conditions. We formally show that for diffuse reection the photometric ratio is invariant to varying camera characteristics, surface albedo, and viewpoint and that therefore the same photometric ratio in both images of a stereo pair implies the same equivalence class of physical constraints. Corresponding photometric ratios along epipolar lines in a stereo pair of images under different illumination conditions is therefore a robust correspondence of equivalent physical constraints, and determination of depth from stereo can be performed without explicitly knowing what these physical constraints being corresponded actually are. This implies a very practical shape-from-stereo methodology applicable to perspective views and not requiring any knowledge whatsoever of illumination conditions. This is particularly practical for determination of 3-D shape on smooth featureless surfaces which has previously been hard to perform using stereo. We demonstrate experimental 3-D shape determination from a dense set of points using our stereo technique on smooth objects of known ground truth shape that are accurate to well within 1% depth accuracy.