6. Homography Computation

If we take two images of a planar surface from two different places, the two images are related by a mapping called a homography. Computing a homography from point correspondences over two images is one of the most fundamental processes of computer vision. This is because, among other things, the 3D positions of the planar surface we are viewing and the two cameras that took the images can be computed from the computed homography. Such applications are discussed in Chaps. 7 and 8. This chapter describes the principles and typical computational procedures for accurately computing the homography by considering the statistical properties of the noise involved in correspondence detection. As in ellipse fitting and fundamental matrix computation, the methods are classified into algebraic (least squares, iterative reweight, the Taubin method, renormalization, HyperLS, and hyper-renormalization) and geometric (FNS, geometric distance minimization, and hyperaccurate correction). We also describe the RANSAC procedure for removing wrong correspondences (outliers).