3D Rotation Estimation from Catadioptric Lines without Correspondences using the Radon Transform, Harmonic Analysis and Conformal Geometric Algebra

Omnidirectional vision systems provide a large field of view, this property can benefit algorithms developed to solve robotic tasks. One interesting problem is the estimation of the rotation between omnidirectional images. Since the images taken by omnidirectional sensors can be mapped to a sphere, the problem of attitude estimation of a 3D camera rotation can be treated as a problem of estimating rotations between spherical images. Usually, this rotation estimation problem has been solved using point correspondences or gradient information of the points of the images. The respective computational time is very time consuming for these point algorithms. In this paper we present an effective solution to the attitude estimation problem with the radon transform, which uses line information instead of points. The algorithm is defined under the conformal geometric algebra framework, to take advantage of the geometric information provided by the omnidirectional projection.