Using Line Correspondence Stereo to Measure Surface Orientation

Accuracy of geometric measurement of object environments for robotic vision tasks is of increasing importance as these tasks become more sophisticated. This paper is concerned with the accurate measurement of orientations of lines and planar surfaces from two camera stereo. Most existing stereo algorithms build up geometric descriptions from absolute position information about points. We emphasize in this paper the accuracy advantages of determining orientation of lines and planar surfaces using the correspondence of linear features instead of point features. Intuitively, the determination of only orientation from absolute position measurement of points uses too much information which requires the unnecessary accurate calibration of certain camera parameters. Orientation information is invariant to knowledge about absolute positional information. If the orientation of lines are computed from the intersection of planar sheets of projection from a stereo pair of cameras, in the absence of all camera errors, the result is independent of baseline. Orientation of planar surfaces can be determined from the cross product of the orientations of at least two coplanar linear features. It is shown that even in the presence of typical camera errors that measurement of the orientations of lines and surfaces using line correspondence stereo is relatively insensitive to base-line errors. Even more, the measurement of orientation from line correspondence stereo is relatively insensitive to typical localization error on the image plane. As a result orientations of lines and planar surfaces far from the baseline can be measured much better using line correspondence stereo rather than point correspondence stereo. 1 Introduction Point correspondence stereo determines the absolute position of points in space, and from these points builds up geometric descriptions of objects. Line correspondence stereo determines the orientation of lines in space without necessarily knowing the absolute position of these lines. In the ideal world, with zero measurement error, the geometric constructions of planes from points and lines are exactly equivalent. So then why bother to analyze another stereo algorithm using equivalent geometric constructions ? The fact is, these geometric constructions are equivalent only in the ideal world. In the real errorful world, where accuracy of measurement is at a premium, orientation measurement of lines and planar surfaces from line correspondence stereo show certain significant superior accuracy properties. Among the advantages of line correspondence stereo over point correspondence stereo, with respect to orientation measurement, are relative insensitivity to baseline errors, and slower error growth rate as the distance from …