Geometry or Featurebased Metrics

Point matching

\( \mathrm{R}=\sum {\left({p}_{A^{\prime }}{p}_B\right)}^2/\mathrm{N} \)

The registration metric R is defined as the sum of the squared distances between corresponding points \( {p}_{A^{\prime }}\ \mathrm{and}\ {p}_B \), where N is the total number of points [16].

Surface matching

\( \mathrm{R}=\sum \mathrm{dist}{\left({p_{A^{\prime}}}^{'},{S}_B\right)}^2/\mathrm{N} \)

The dist (\( {p}_{A^{\prime }} \), S_{B}) computes the (minimum) distance between point \( {p}_{A^{\prime }} \) and the surfaces S_{B}, N is the number of points in Study A [16].

Intensitybased Metrics

Sum of Squared Differences (SSD)

\( \mathrm{SSD}=\sum {\left({I}_{A^{\prime }}{I}_B\right)}^2/\mathrm{N} \)

The SSD metric is defined as the average squared intensity (\( {I}_{A^{\prime }} \) and I_{B}) difference between Study A and Study B, where N is the number of evaluated voxels [16].

Correlation Coefficient (CC)

CC=\( \frac{\sum_{\overrightarrow{x}}\left(A\left(\overline{x}\right)\overline{A}\right)\left(T\left(B\left(\overrightarrow{x}\right)\right)\overline{B}\right)}{\sqrt{\sum_{\overrightarrow{x}}{\left(A\left(\overline{x}\right)\overline{A}\right)}^2{\sum}_{\overrightarrow{x}}{\left(T\left(B\left(\overrightarrow{x}\right)\right)\overline{B}\right)}^2}} \)

CC measures the similarity in the image signal, which assumes a linear relationship between voxel intensities in two images [16].

Mutual Information (MI)

\( \mathrm{MI}\ \left({I}_{A^{\prime }},{I}_B\right)=\sum \limits_{\mathrm{B}}\sum \limits_Ap\left({I}_{A^{\prime }},{I}_B\right){\mathit{\log}}_2\left[p\left({I}_{A^{\prime }},{I}_B\right)/p\left({I}_{A^{\prime }}\right)p\left({I}_B\right)\right] \)

MI has proven very effective for registering image data from different modalities, where p (I_{A’}) and p (I_{B}) are the probability distribution functions of the intensities I_{A’} and I_{B}, respectively, and \( p\left({I}_{A^{\prime }},{I}_B\right) \) is the joint probability distribution function [16].
