Omnidirectional catadioptric image unwrapping via total variation regularization

A catadioptric sensor is composed of a hyperbolic mirror coupled with a camera. The registered images with such sensor have a field of view of 360 degrees; this property is very useful in robotics since it increases a robot´s performance for navigation and localization. However, due to the significant distortions on the omnidirectional image, classical image processing can not be directly applied onto the image. The standard techniques to unwrap catadioptric images involve a projection step follow by an interpolation step. In this paper we propose to unwrap omnidirectional images via Total Variation (TV) regularization by casting the geometric projection as the forward operator. This has two advantages: if the acquired images are noisy (due to dust onto the mirror or wireless transmission errors), the noise can be effectively remove while the unwrapping step is performed; moreover if the mirror or camera´s lenses have any type of aberrations they could be included as part of the forward operator and then compare the standard unwrapping method with our proposed (TV based) method and show the superior reconstruction quality of the proposed method when the acquired images are corrupted with salt-and-pepper noise.