Geometric invariants and applications under catadioptric camera model

This paper presents geometric invariants of points and their applications under central catadioptric camera model. Although the image has severe distortions under the model, we establish some accurate projective geometric invariants of scene points and their image points. These invariants, being functions of principal point, are useful, from which a method for calibrating the camera principal point and a method for recovering planar scene structures are proposed. The main advantage of using these invariants for plane reconstruction is that neither camera motion nor the intrinsic parameters, except for the principal point, is needed. The theoretical correctness of the established invariants and robustness of the proposed methods are demonstrated by experiments. In addition, our results are found to be applicable to some more general camera models other than the catadioptric one