3-DIMENSIONAL STEREO BY PHOTOMETRIC RATIOS

We present a novel robust methodology for corresponding a dense set of points on an object surface from photometric values for three-dimensi onal stereo computation of depth. The methodology utilizes multiple st ereo pairs of images, with each stereo pair being taken of the identic al scene but under different illumination. With just two stereo pairs of images taken under two different illumination conditions, respectiv ely, a stereo pair of ratio images can be produced, one for the ratio of left-hand images and one for the ratio of right-hand images. We dem onstrate how the photometric ratios composing these images can be used for accurate correspondence of object points. Object points having th e same photometric ratio with respect to two different illumination co nditions constitute a well-defined equivalence class of physical const raints defined by local surface orientation relative to illumination c onditions. We formally show that for diffuse reflection the photometri c 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. The correspondence of photometric ratios along epipolar lines in a stereo pair of images under different illumination conditio ns is therefore a robust correspondence of equivalent physical constra ints, and the determination of depth from stereo can be performed with out explicit knowledge of what these corresponding physical constraint s actually are. Whereas illumination planning is required, our photome tric-based stereo methodology does not require knowledge of illuminati on conditions in the actual computation of three-dimensional depth and is applicable to perspective views. This technique extends the stereo determination of three-dimensional depth to smooth featureless surfac es without the use of precisely calibrated lighting. We demonstrate ex perimental depth maps from a dense set of points on smooth objects of known ground-truth shape, determined to within 1% depth accuracy.