3D Reconstruction from Multiple Images

Suppose that a fixed scene is seen by two or more perspective cameras. We are interested in geometric issues, so we will suppose that the correspondences between visible points in different images are already known. However it must be pointed out that matching is a fundamental and extremely difficult issue in vision, which can not be dismissed so lightly in practice.

So in this section, we suppose that n 3D points A_i are observed by m cameras with projection matrices $P_{j}, j= 1,\ldots,m$. Neither the point positions nor the camera projections are given. Only the projections a_ij of the i^th point in the j^thimage are known.