Epipolar curves on surfaces

Abstract The view lines associated with a family of profile curves of the projection of a surface onto the retina of a moving camera defines a multi-valued vector field on the surface. The integral curves of this field are called epipolar curves, and together with a parametrization of the profiles 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 gives a systematic way of detecting the gaps left by reconstruction of a surface from profiles. They also suggest methods for filling in these gaps.

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