Euclidean means the Euclidean distance, i.e., the mean squared difference between the gray values of model and reference.

This metric computes values between and 0. Images closer to each other will have a metric closer to 0. where are the individual voxels and is the voxel count.

Correlation measures the correlation ratio of the registered images.

This metric computes values between 0 and 1. The case correlation ratio = 1 corresponds to the case of two identical and registered images. where is the voxel mean.

The mutual information measures the information shared by both images.

This metric computes values between 0 and . For instance, if images are independent, knowing does not give any information about and vice versa, so their mutual information is zero.

The mutual information metrics, especially the normalized one, are recommended when images from different modalities, e.g., CT and MRT, are to be registered.

The mutual information is: Where and are the marginal entropies of the image histrograms and is the joint entropy of the image histograms.