The earliest multi-modality surface-based registration algorithm was the "head-and-hat" algorithm proposed by Pelizzari et al. . This algorithm was used to align MRI, CT, and PET images of the head. The high-resolution CT or MR image was represented as a stack of disks, referred to as the "head". The second surface was represented as a list of unconnected 3D points, the "hat". The registration transformation was then determined by iteratively transforming the "hat" points until the closest fit of hat on head was found. The measure of closeness of fit was the sum of squared distances between a point on the hat and the nearest point on the head, in the direction of the centroid of the head. The original algorithm used Powell optimization , which involves a sequence of one-dimensional optimizations along each of the six degrees of freedom of the rigid-body transformation. The algorithm stopped when it failed to find a solution in any of the degrees of freedom that improved the measure of fit by more than a predefined tolerance. The corresponding surfaces most commonly used were the skin surface from MRI and PET transmission images or the brain from MRI and PET emission images. The algorithm proved to be reasonably robust but was prone to error with convoluted surfaces and was particularly susceptible to errors in cranio-caudal rotation due to the natural symmetry of the cranium mentioned above. It requires a reasonably good first guess or "starting estimate" of the correct registration transformation. In most cases, the known patient orientations in the scanners will suffice. The method has also been applied to cardiac MRI and PET images of the heart .
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