Cross Correlation

Cross-correlation was one of the first cost functions used for image registration [18]. This cost function first multiplies the intensities of the two images at each voxel and sums the resulting product. The product is then normalized by dividing it by the product of the root mean squared intensities of each of the two images. If the images are identical, the resulting value will be equal to 1. Differences in the images will produce values less than 1. It should be noted that the cross-correlation measure does not explicitly compensate for differences in image intensity, and it is possible that images identical except for global scaling may not reach an optimum in the cost function unless a variable scaling parameter is formally included in the model. Implementations of cross-correlation have generally not used calculus-based minimization methods (e.g., Collins etal. [4] use simplex minimization), and our own attempts to implement calculus-based minimization of this cost function have not given good results. The added efficiency of calculus-based minimization methods has tended to make the cross-correlation cost function less commonly used.

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