An Introduction to Mathematical and Statistical Methods of Medical Image Registration – A Review

The purpose of this paper is to present a survey of recent works concerning medical image registration techniques and some central mathematical and statistical problems in medical imaging. It will be classified according to a model based on nine salient criteria, the main dichotomy of which is extrinsic versus intrinsic methods. The statistics of the classification show definite trends in the evolving registration techniques, which will be discussed. After defining the medical image registration problem, we provide a short introduction to a select group of multi-modal image alignment approaches. More precisely, we choose four widely-used statistical methods applied in registration scenarios for analysis and comparison. We clarify the implicit and explicit assumptions made by each, aiming to yield a better understanding of their relative strengths and weaknesses. We will also discuss how mathematics may impact some of the main problems in this area, including image enhancement, registration, and segmentation.