Abstract

We present a novel robust methodology for corresponding a dense set of points on an object surface from photometric values for three-dimensional stereo computation of depth. The methodology utilizes multiple stereo pairs of images, with each stereo pair being taken of the identical scene but under different illumination. With just two stereo pairs of images taken under two different illumination conditions, respectively, 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 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 two different illumination conditions constitute a well-defined equivalence class of physical constraints defined by local surface orientation relative to illumination conditions. We formally show that for diffuse 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. The correspondence of 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 the determination of depth from stereo can be performed without explicit knowledge of what these corresponding physical constraints actually are. Whereas illumination planning is required, our photometric-based stereo methodology does not require knowledge of illumination 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 surfaces without the use of precisely calibrated lighting. We demonstrate experimental depth maps from a dense set of points on smooth objects of known ground-truth shape, determined to within 1% depth accuracy.

© 1994 Optical Society of America

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