A Condition Number for Point Matching with Application to Registration and
Post-Registration Error Estimation

 

* Dept. of Electrical and Computer Engineering
University of California at Santa Barbara
Santa Barbara, CA 93106
Email: {kenney, manj, zuliani}@ece.ucsb.edu

** Research Department
Naval Air Warfare Center Weapons Division, Code 4T4100D
China Lake, CA 93555-6100
Email: {hewerga, vannevelaj}@navair.navy.mil

Abstract

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.