Abstract

We present in this chapter applications of condition theory for image registration problems in a general framework that is easily adapted to a variety of image processing tasks. After summarizing the history and foundations of condition theory, a short analysis is given of computational sensitivity for point correspondence between images with respect to translation, rotation-scale-translation (RST), and affine pixel transforms. Several surprising results follow from this analysis, including the principal result that increasing transform complexity is mirrored by increasing computational sensitivity, i.e., KTrans ≤ KRST ≤ KAffine. The utility of condition-based corner detectors is also seen in the demonstrated equivalence between the translational condition number and the commonly used Shi-Tomasi corner function. These results are supplemented by a short discussion of sensitivity estimation for the computed transform parameters and any resulting registration misalignment.

Introduction

The central issue in image registration is the problem of establishing correspondence between image features, whether they are point features (e.g., corner locations) or extended features (e.g., level sets). Corresponding features then act as input for the process of computing a low-dimensional pixel map between images. The success of this approach depends on the accuracy of the feature correspondence, in the sense that mismatched features can lead to completely erroneous transform estimates. Mismatches may be due to computational constraints that limit the complexity of the feature-matching algorithm or may be intrinsic to the image pair as is the case with identical local features, such as windows in an office building.