On the Epipolar Geometry in Stereo Vision

In this paper we are interested in the calculation of the equation governing pairs of epipolar lines for unregistered images, i.e. when the image acquisition parameters are unknown or no calibration object is available. First we do a thorough analysis of the mathematics required to nd the epipolar line equations in the classical sense. Thereafter we show that for a broad class of stereo images the epipolar line equation can be obtained directly from the images without restrictive assumptions on the stereo geometry and without anyone 3D reference point. Therefore, the estimation of the epipolar line equations reduce to solve a linear optimization problem. Finally, we give an eecient algorithm to nd the epipolar line equations directly from the image data, without knowledge of the image acquisition parameters.