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FIGURE 1. Concept of image registration based on mutual information (MI) is explained using example of PET and CT. Separate PET and CT image intensity histograms are derived from PET and CT, which contain frequencies (f) of occurrence for specific voxel values in 3D volumes (p = PET, c = CT). Additional 2D image histogram is created from combination of PET and CT data, in which frequencies of occurrence for particular PET/CT voxel intensity pairs (p, c), both at same location, are calculated. Subsequently, PET and CT image entropies are calculated from PET and CT histograms, and 2D PET/CT histogram is used to calculate joint entropy. Joint entropy is smallest and, consequently, MI is largest when images are closely aligned and 2D histogram is least dispersed. Search is performed, which continuously modifies 3D shifts (X,Y,Z) and rotations (XY, XZ, YZ), each time transforming PET data. Although it is possible to perform image registration using joint entropy only, inclusion of separate PET and CT entropies is needed when portions of PET volume could move outside of overlapping field of view.
