Epipolar geometry of catadioptric stereo systems with planar mirrors

In order to simplify the design and implementation of a stereo vision system, catadioptric instruments have been used to capture stereo images with a single camera. These catadioptric stereo systems not only provide radiometric advantages over traditional two-camera stereo, but also reduce the complexity and cost of acquiring stereoscopic video. Although much research has been done on the design of the catadioptric stereo system, little attention has been paid to analyze the planar catadioptric stereo (PCS) system based on the epipolar geometry. In this paper, we investigated characteristics of a selected PCS system and proved that it can be approximated by affine epipolar geometry. This affine model reduces the number of parameters in the fundamental matrix from seven in the conventional stereo system to only four in the PCS system. Experimental results verify that estimation of the fundamental matrix for a PCS system can be more robust, precise, and much easier to implement with the affine model. Furthermore, rectification of the image pair based on the affine fundamental matrix can achieve better performance with much less geometric distortion. These significant advantages confirm the usefulness of an affine fundamental matrix model for the selected PCS system.