12 - Gradient descent approaches to image registration

Summary

Abstract

This chapter covers a general class of image registration algorithms that apply numerical optimization to similarity measures relating to cumulative functions of image intensities. An example of these algorithms is an algorithm minimizing the least-squares difference in image intensities due to an iterative gradient-descent approach. Algorithms in this class, which work well in 2D and 3D, can be applied simultaneously to multiple bands in an image pair and images with significant radiometric differences to accurately recover subpixel transformations. The algorithms discussed differ in the specific similarity measure, the numerical method used for optimization, and the actual computation used. The similarity measure can vary from a measure that uses a radiometric function to account for nonlinear image intensity differences in the least-squares equations, to one that is based on mutual information, which accounts for image intensity differences not accounted for by a standard functional model. The numerical methods considered are basic recursive descent, a method based on Levenberg-Marquardt's technique, and Spall's algorithm. This chapter relates to the above registration algorithms and classifies them by their various elements. It also analyzes the image classes for which variants of these algorithms apply best.

Introduction

We consider in this chapter a class of image registration algorithms that apply numerical techniques for optimizing some similarity measures that relate only to the image intensities (or a function of the image intensities) of an image pair.