Systematic Curvature Distortions in Stereo

Systematic distortions occur when incorrect parameters of a stereo configuration are used in the reconstruction of a three-dimensional scene from image correspondences. Consideration of the effect of errors on reconstruction is especially important for an active observer, since its stereo configuration changes continuously due to gaze shifts, and hence needs to be recomputed in real-time. For a fixating observer the largest distortions occur within epipolar planes; of particular interest among these is the fixation plane. We study the distortion of points in this plane on a global, qualitative, level, making use of properties of quadratic Cremona transformations, and on a local, quantitative level. We derive closed-form expressions for the distortion of curvature and determine the exact criteria governing changes in convexity of curves. Our simulations show that such distortions can be severe for very close distances; for the most part, however, curvature distortion depends roughly linearly on the fixation error, but only marginally on fixation angle or distance along the gaze line.