Analytic image unwarping by a systematic calibration method for omni-directional cameras with hyperbolic-shaped mirrors

Unwarping an omni-directional image into a perspective-view one is easy for a single-viewpoint (SVP) designed catadioptric omni-directional camera. But misalignment between the components (such as the mirror and the lens) of this kind of camera creates multiple viewpoints and distorts the unwarped image if the SVP constraint is assumed. The SVP constraint is relaxed in this study and a systematic method is proposed to derive a set of new and general analytic equations for unwarping images taken from an omni-directional camera with a hyperbolic-shaped mirror (called a hypercatadioptric camera). The derivation is made possible by careful investigation on the system configuration and precise calibration of involved system parameters. As a verification of the correctness of the derived equations, some of the system parameters are adjusted to fit the SVP constraint, and unwarped images using the resulting simplified camera model are shown to be of no difference from those obtained by a method based on the SVP model. The generality of the proposed method so has extended the image-unwarping capability of the existing methods for the hypercatadioptric camera to tolerate lens/mirror assembly imprecision, which is difficult to overcome in most real applications. Some experimental results of image unwarping are also included to show the effectiveness of the proposed method.