Distance Metric Learning for Medical Image Registration

Medical image registration has received considerable attention in medical imaging and computer vision, because of the large variety of ways in which it can impact patient care. Over the years, many algorithms have been proposed for medical image registration. Medical image registration uses techniques to create images of parts of the human body for clinical purposes. This thesis focuses on one small subset of registration algorithms: using machine learning techniques to train the similarity measure for use in medical image registration. This thesis is organized in the following manner. In Chapter 1 we introduce the idea of image registration, describe some some applications in medical imaging, and mathematically formulate the three main components of any registration problem: geometric transformation, similarity measure and optimization procedure. Finally we describe how the ideas in this thesis fit into the field of medical image registration, and we describe some related work. In Chapter 2 we introduce the concept of machine learning and we provide examples to illustrate machine learning algorithms. We then describe the κ-nearest neighbors algorithm and the relationship between Euclidean and Mahalanobis distance. Next we introduce distance metric learning and present two approaches for learning the Mahalanobis distance. Finally we provide a description and visual comparison of two algorithms for distance metric learning. In Chapter 3 we describe how distance metric learning can be applied to the problem of medical image registration. Our goal is to learn the optimal similarity measure given a training dataset of correctly registered images. To assess the performance of the two distance metric learning algorithms we test them using images from a series of patients. Moreover we illustrate the sensitivity of one of the learning algorithms by examining the variability of the resulting target registration errors. Finally we present our experimental results of registering CT and MR images. Finally in Chapter 4 we suggest some ideas for future work in order to improve our registration results and to speed up the algorithms.