Projection model, 3D reconstruction and rigid motion estimation from non-central catadioptric images

This paper addresses the problem of rigid motion estimation and 3D reconstruction in vision systems where it is possible to recover the incident light ray direction from the image points. Such systems include pinhole cameras and catadioptric cameras. Given two images of the same scene acquired from two different positions, the transformation is estimated by means of an iterative process. The estimation process aims at having corresponding incident rays intersecting at the same 3D point. Geometrical relationships are derived to support the estimation method. Furthermore, this paper also addresses the problem of the mapping from 3D points to image points, for non-central catadioptric cameras with mirror surfaces given by quadrics. The projection model presented can be expressed in a non-linear equation of only one variable, being more stable and easier to solve than the classical Snell´s law. Experiments with real images are presented, by using simulated annealing as estimation method.