On the multiple-view triangulation problem with perspective and non-perspective cameras: a virtual reprojection-based approach

Abstract

This paper considers the multiple-view triangulation problem in a vision system with perspective and nonperspective cameras. In particular, cameras that can be modeled through a spherical projection followed by a perspective one, such as perspective cameras and fisheye cameras, are considered. For this problem, an approach based on reprojecting the available image points onto virtual image planes is proposed, which has the advantage of transforming the original problem into a new one for which the existing methods for multipleview triangulation with perspective cameras can be used. In particular, algebraic and geometric errors of such methods are now evaluated on the virtual image planes, and the solution of the new problem exactly approaches the sought scene point as image noise and calibration errors tend to zero. The proposed approach is illustrated by several numerical investigations with synthetic and real data.