 
Summary: 3D Stereo Using Photometric Ratios
Lawrence B . Wolff
Elli Angelopoulou
Computer Science Department
The Johns Hopkins University
Baltimore, Maryland 21218
ABSTRACT
We present a novel robust methodology for corresponding a dense set of points on an object surface from photometric values,
for 3D 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 2different 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 welldefined equivalence
class of physical constraints defined by local surface orientation relative to illumination conditions. We formally show that for dif
fuse reflection 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. Correspond
ing 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 shapefromstereo method
ology applicable to perspective views and not requiring any knowledge whatsoever of illumination conditions. This is particularly
