Reconstruction from Image Correspondences

The data for reconstruction from image correspondences consist of corresponding points from two images of the same scene taken from different viewpoints. A point in the first image corresponds to a point in the second image if and only if both points are projections of the same point in space. Reconstruction is the task of finding the relative positions of the two viewpoints compatible with the image correspondences. If sufficiently many image correspondences in general position are available then the relative position is determined up to a single unknown scale factor and a single 180° twist about the line joining the optical centres of the two cameras. There are many mathematically equivalent ways of formulating reconstruction. The imaging surface can be a plane or a sphere or some other more complicated shape. The rotation of the camera can be described using orthogonal matrices or quaternions and the geometry of reconstruction can be described in terms of Euclidean or projective geometry. The different formulations are equivalent, in that it is straightforward to translate from one formulation to another.