#### Distinguished Lecture

# Some Analysis and Applications of Image Registration

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When a sequence of images are taken by a camera that is moving or when the scene contains objects that are moving, the images often need to be aligned or registered with each other for purposes of further processing. Indeed image registration is often a required precursor to many other sophisticated image and video processing operations.

I will present some recent results on this problem in two application domains.

First, I give results on the growth of the error in registering a sequence of images. Attention is restricted to the simple and somewhat restrictive class of 2-D translations. However, the main objective is not to study the registration problem itself but rather the growth rate of the registration error as the number of images in the sequence increases. Restricting attention to the simple class of 2-D translations allows us to make analytical headway on this problem. The problem is posed as an estimation problem on a graph. A real valued function on the nodes of the graph is to estimated from noisy differential measurements of the function values. Two cases of particular interest are the linear graph and a circular graph with N nodes. The main result is that increasing the size of the local group of nodes over which measurement is performed has a significant effect on the accumulation of the registration error. We show this through approximation, upper bounds on error growth, and in some special cases by closed form expressions for the worst case error variance.

A second motivating application is the registration of images from different modalities, e.g. MRI with PET images. Time permitting, I will discuss some observations on registration metrics and computational issues and presented a new algorithm that is grounded in the Euclidean minimal spanning tree estimation of entropy.