Geometry and Shape I
Epipolar fields on surfaces
Peter J. Giblin1 and Richard S. Weiss2
| (1) |
Dept. of Pure Mathematics, University of Liverpool, L69 3BX Liverpool, England |
| (2) |
Dept. of Computer Science, University of Massachusetts, 01003 Amherst, MA, USA |
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. This parametrization has been used in the systematic reconstruction of surfaces from their profiles. We present a complete local investigation of the epipolar curves, including their behaviour in a neighbourhood of a point where the epipolar parametrization breaks down. These results give a systematic way of detecting the gaps left by reconstruction of a surface from profiles. They also suggest methods for filling in these gaps.
Both authors would like to thank the Newton Institute in Cambridge, England, for providing an excellent environment for us to work together, and NATO grant CRG 910221. In addition, the second author would like to acknowledge the support of DARPA and TACOM under contract DAAE07-91-C-R035 and NSF under grants IRI-920892 and IRI-9116297.
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