Least Squares and Scaled Least Squares

Another index of image similarity is the squared difference in image intensities averaged across all voxels. This value should be minimal when the images are registered. If large differences in image intensity are present, a global scaling term can be added as an additional parameter to be optimized. Calculus-based minimization is especially robust for least squares problems, making this cost function especially attractive and easy to implement [1,8,10,11,12,21,22]. Even for highresolution MRI registration, this cost function is able to produce subvoxel accuracy [21] and it is sufficiently robust to allow spatial transformation models with hundreds of parameters to be optimized [22].

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