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 KTrans ≤ KRST ≤ KAffine. 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 KTrans is easily computed whereas KRST and KAffine 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–multi-date Landsat images, aerial images, aerial videos, and infra-red images. A web site where the users can try our registration software is available and is being actively used by researchers around the world. Index Words: Registration, Conditioning, Feature representation, Motion This research was supported by the Office of Naval Research under ONR Grant Number N00014-02-1-0318. January 7, 2004 Submitted to PAMI