A condition number for point matching with application to registration and postregistration error estimation

Selecting salient points from two or more images for computing correspondence is a well-studied problem in image analysis. This paper describes a new and effective technique for selecting these tiepoints using condition numbers, with application to image registration and mosaicking. Condition numbers are derived for point-matching methods based on minimizing windowed objective functions for 1) translation, 2) rotation-scaling-translation (RST), and 3) affine transformations. Our principal result is that the condition numbers satisfy K_Trans ≤ K_RST ≤ K_Affine. That is, if a point is ill-conditioned with respect to point-matching via translation, then it is also unsuited for matching with respect to RST and affine transforms. This is fortunate since K_Trans is easily computed whereas K_RST and K_Affine are not. The second half of the paper applies the condition estimation results to the problem of identifying tiepoints in pairs of images for the purpose of registration. Once these points have been matched (after culling outliers using a RANSAC-like procedure), the registration parameters are computed. The postregistration error between the reference image and the stabilized image is then estimated by evaluating the translation between these images at points exhibiting good conditioning with respect to translation. The proposed method of tiepoint selection and matching using condition number provides a reliable basis for registration. The method has been tested on a large number of diverse collection of images - multidate Landsat images, aerial images, aerial videos, and infrared images. A Web site where the users can try our registration software is available and is being actively used by researchers around the world.