Cheirality in epipolar geometry

Abstract

The image points in two images satisfy epipolar constraint. However, not all sets of points satisfying epipolar constraint correspond to any real geometry because there can exist no cameras and scene points projecting to given image points such that all image points have positive depth. Using the cheirability theory due to Hartley and previous work an oriented projective geometry, we give necessary and sufficient conditions for an image point set to correspond to any real geometry. For images from conventional cameras, this condition is simple and given in terms of epipolar lines and epipoles. Surprising, this is not sufficient for central panoramic cameras. Apart from giving the insight to epipolar geometry, among the applications are reducing the search space and ruling out impossible matches in stereo, and ruling out impossible solutions for a fundamental matrix computed from seven points.