Epipolar curves on surfaces

The view lines associated with a family of proole curves of the projection of a surface onto the retina of a moving camera deenes a multi-valued vector eld on the surface. The integral curves of this eld are called epipolar curves and together with a parametrization of the prooles provide a parametrization of regions of the surface. We present an investigation of epipolar curves on the object surface and in a related`spatio-temporal surface'. We also consider the epipolar constraint in the image and the resulting epipolar curves there. In particular we make an exhaustive list of the circumstances where the epipolar parametrization breaks down. These results give a systematic way of detecting the gaps left by reconstruction of a surface from prooles. They also suggest methods for lling in these gaps.