Postprint version. Published in Mathematical Biosciences and Engineering, Volume 3, Issue 2, April 1, 2006, pages 389-418.
Copyright © 2006 American Institute of Mathematical Sciences. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Mathematical Biosciences and Engineering following peer review. The definitive publisher-authenticated version is available online at http://aimsciences.org/journals/displayPapers.jsp?comments=&pubID=120&journID=8&pubString=Volume:%203,%20Number:%202,%20April%202006.
NOTE: At the time of publication, the author Dana Paquin was not yet affiliated with Cal Poly.
A multiscale image registration technique is presented for the registration of medical images that contain significant levels of noise. An overview of the medical image registration problem is presented, and various registration techniques are discussed. Experiments using mean squares, normalized correlation, and mutual information optimal linear registration are presented that determine the noise levels at which registration using these techniques fails. Further experiments in which classical denoising algorithms are applied prior to registration are presented, and it is shown that registration fails in this case for significantly high levels of noise, as well. The hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and L. Vese  is presented, and accurate registration of noisy images is achieved by obtaining a hierarchical multiscale decomposition of the images and registering the resulting components. This approach enables successful registration of images that contain noise levels well beyond the level at which ordinary optimal linear registration fails. Image registration experiments demonstrate the accuracy and efficiency of the multiscale registration technique, and for all noise levels, the multiscale technique is as accurate as or more accurate than ordinary registration techniques.