Localization of 3D lines from single images using off-axis catadioptric cameras

The reconstruction of 3D scenes constituted by straight lines can find many applications both in Computer vision and in Mobile robotics. Most approaches to 3D reconstruction analyze several images, which need the determination of the correspondences between the used images. This paper studies the localization of straight lines in 3D space from single 2D images, acquired by a noncentral catadioptric camera. In general, using a noncentral camera, the viewing rays starting from the points of a straight line constitute a nonplanar surface: if this non-planar surface only contains a finite number of straight line, other than the viewing rays, then the straight line can be localized (up to a finite number of solutions). In a previous work we dealt with line localization using an axial-symmetric catadioptric camera. In this paper the axial-symmetry constraint is relaxed, since the camera is placed at a generic position relative to an axial-symmetric mirror. The geometrical conditions for line localization are derived for off-axis catadioptric cameras based on a conic mirror, and some preliminary experimental results are presented.