Geometry or Feature-based 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 .
Surface matching $$\mathrm{R}=\sum \mathrm{dist}{\left({p_{A^{\prime}}}^{'},{S}_B\right)}^2/\mathrm{N}$$ The dist ($${p}_{A^{\prime }}$$, SB) computes the (minimum) distance between point $${p}_{A^{\prime }}$$ and the surfaces SB, N is the number of points in Study A .
Intensity-based 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 IB) difference between Study A and Study B, where N is the number of evaluated voxels .
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 .
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 (IA’) and p (IB) are the probability distribution functions of the intensities IA’ and IB, respectively, and $$p\left({I}_{A^{\prime }},{I}_B\right)$$ is the joint probability distribution function .