Ratio Image Uniformity

A cost function that does allow for global differences in image intensity without the need for formal modeling of an intensity scaling parameter is the ratio uniformity cost function introduced in 1992 [20]. If one image is divided by the other image on a voxel-by-voxel basis, the resulting ratio image should have a constant uniform value when the images are well registered. Any misregistration will induce nonuniformities. The ratio image cost function quantifies this lack of uniformity by computing the standard deviation of the ratio image and normalizing the result by the mean ratio. This cost function is amenable to calculus-based registration and has been validated extensively for intramodality registration of PET images and MRI images [13,20,21]. Recent work [21] has shown that this cost function does not perform as well for MRI registration as the scaled least squares cost function discussed next, but it is slightly better than the scaled least squares cost function for registration of PET images of a realistic brain phantom. A simulation study comparing the ratio image uniformity measure to other selected registration methods that were not based on voxel intensities showed good performance by the ratio image uniformity cost function [19].

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