Moving towards the horizon of a planar curve

Abstract

The use of the horizon of a planar and convex curve has been discussed. The spatial orientation of the curve plane and of any curve tangent may be determined unambiguously from image coordinates in one image. Curve points may be matched geometrically from two images of an image sequence, produced by translation or acceleration, which does not produce rotation. The focus of expansion during translation may be constructed geometrically from two images. Spatial position and velocity of a curve point may be determined unscaled, if the spatial acceleration is known and the optic flow and optic acceleration are nonzero and nonaligned. Any of these determination schemes are unambiguous and involve very few calculations. Algorithms have been suggested for the determination of the horizon from an image sequence, where the horizon is not visible.<>