Introduction

Intensity based cost functions, also called voxel similarity measures, have recently come to dominate the field of cross-modality or intermodality medical image registration. For same modality or intramodality registration, techniques that align images by optimizing some measure of image similarity calculated from the original voxel intensity values of the images have an intuitive basis. For intermodality registration, however, the intensity values in images of the same object taken with the different modalities are often very different, so the success of voxel similarity measures in this area is surprising. In this chapter, we give some background for the use of intensity-based cost functions in intermodality image registration, and describe how information theoretic measures, in particular mutual information, came to be used. We discuss the successes of mutual information and highlight situations when it fails. The most widely used application of intermodality registration is aligning three-dimensional MR, CT, SPECT, and PET images of the head. In this case, the registration transformation is usually assumed to have the six degrees of freedom of rigid-

body motion. Most of the discussion is, however, applicable for registration transformations involving different numbers of degrees of freedom. For example, some researchers are interested in aligning 2D projection images (e.g., X-rays or video images) with 3D images, so called 2D-3D registration. Other authors add scaling or skew degrees of freedom in order to model poorly calibrated voxel dimensions or CT gantry tilt. Mutual information has also been used to control registration incorporating elastic deformation (sometimes called free-form deformation), but few intermodality results have so far been produced. Although most of the results presented in this chapter come from the main application area of 3D rigid body registration, we also include results from other application areas.

Intermodality registration differs in several important ways from intramodality registration. Almost by definition, different medical imaging modalities usually have quite different intensity characteristics. Also, whereas images from the same modality being registered are frequently acquired with very similar resolutions and fields of view (especially in serial MR applications), intermodality images often differ substantially from each other in both these respects. The modalities are often most different in resolution and field of view in the through-slice direction, where, for example, a much smaller volume of CT data than MR data might have been acquired because of radiation dose considerations. As a consequence, the volume of overlap of the two images may be considerably smaller than the volume imaged by either modality. To be clinically useful, it is important that any intermodality registration algorithm can be successfully applied to images of this sort.

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