A Geometric Approach to Multiple-View Triangulation for Fisheye Cameras

It is well-known that fisheye cameras can be very useful in real applications due to their large field of view when compared to classic perspective cameras. This paper considers the fundamental problem of multiple-view triangulation for fisheye cameras. A geometric criterion is introduced in this paper for this problem, which consists of determining the scene point that minimizes the angles between the projections of the available image points and of the sought point itself. A solution based on convex optimization is proposed in this paper for this criterion, which consists of solving an eigenvalue problem. Numerical investigations carried out with synthetic and real data suggest that the proposed criterion provides significantly better estimates than algebraic criteria.