Abstract

We investigate the influence of the mirror shape on the imag- ing 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 an- alytical expressions for the two limiting surfaces of this “virtual image zone”. This is difierent 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 difierent 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 difiers from a similar configuration proposed by Ollis et al. [2]. We calculate the caus- tic surfaces and show that this stereo con?guration can be approximated by two single view points yielding an e?ective vertical stereo baseline of approx. 3.7 cm. An example of panoramic disparity computation using a physiologically motivated stereo algorithm is given.