The Quality of Catadioptric Imaging ? Application to Omnidirectional Stereo

We investigate the influence of the mirror shape on the imaging quality of catadioptric sensors. For axially symmetrical mirrors we calculate the locations of the virtual image points considering incident quasi-parallel light rays. Using second order approximations, we give analytical expressions for the two limiting surfaces of this “virtual image zone”. This is different to numerical or ray tracing approaches for the estimation of the blur region, e.g. [1]. We show how these equations can be used to estimate the image blur caused by the shape of the mirror. As examples, we present two different omnidirectional stereo sensors with single camera and equi-angular mirrors that are used on mobile robots. To obtain a larger stereo baseline one of these sensors consists of two separated mirror of the same angular magnification and differs from a similar configuration proposed by Ollis et al. [2]. We calculate the caustic surfaces and show that this stereo configuration can be approximated by two single view points yielding an effective vertical stereo baseline of approx. 3.7 cm. An example of panoramic disparity computation using a physiologically motivated stereo algorithm is given.