Discrete epipolar geometry

The epipolar geometry, which lies in the basis of 3D reconstruction techniques in the field of computer vision, is formulated in continuous spaces and gives geometric relationships between different views of a point in space. In applications, however, we cannot deal with points themselves in digital images. This is because digital images involve some digitization process and the smallest unit in digital images is a pixel. In this paper, we propose a discrete version of the epipolar geometry, called the discrete epipolar geometry, that gives geometric relationships between pixels rather than points. We then apply this discrete epipolar geometry to 3D reconstruction.