3D geometry from planar parallax

Abstract

Deriving 3D structure in a fixed object-centered coordinate system is an increasingly popular trend in shape from multiple views. For linear approximations to perspective projection (weak/para perspective), and for the case of image velocities, elegant linear methods have been devised for robust estimation. For reconstruction under arbitrary view transformations, linear projective methods using point correspondences have been suggested. In this paper, we formulate the problem of intrinsic 3D structure estimation through perspective projection using motion parallax, defined with respect to an arbitrary plane in the environment. It is shown that if an image coordinate system is warped using plane projective transformation with respect to a reference view, the residual image motion is dependent only on the epipoles and has a simple relation to the 3D structure. Our computational scheme avoids point/line correspondence and is based on hierarchical estimation and image warping working directly with spatio-temporal image intensities.