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Epipolar geometry for conics


This 3D figure shows the epipolar geometry for two perspective images of a conic. It is done for a special case: the conic in the scene is obtained by projecting a circle from a laser projector, onto a plane in the scene. The circle's projection is then imaged by a camera. The epipolar constraint for the imaged conic is as follows. There are in general two epipolar lines which are tangent to the circle in the laser's (virtual) image plane. The associated epipolar lines in the camera image (shown in cyan), must be tangent to the imaged conic. The figure also shows a conic in green. It means the following. The optical centers of camera and laser span, together with the imaged conics (circle in the case of the laser), cones. The two cones intersect, by construction, in the conic on the scene plane where the laser projects on. However, the cones also intersect, in general, in a second conic in the scene, the one shown in green.