Table 1.

A summary of popular quantitative measures of brain MRI segmentation quality and their mathematical formulation with respect to the number of false positives (FP), true positives (TP), and false negatives (FN) at voxel level and lesion level (FPL, TPL, and FNL, respectively). ∂S and ∂R are the sets of lesion border pixels/voxels for the tested and the reference segmentations, and d_m(v, V) is the minimum of the Euclidean distances between a voxel v and voxels in a set V.

Metric of segmentation quality	Mathematical description
True positive rate, TPR	$\mathrm{TPR}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}$
Positive predictive rate, PPV	$\mathrm{PPV}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}$
Dice similarity coefficient, DSC	$\mathrm{DSC}=\frac{2\mathrm{TP}}{2\mathrm{TP}+\mathrm{FP}+\mathrm{FN}}$
Volume difference rate, VDR	$\mathrm{VDR}=\frac{\mid \mathrm{FP}-\mathrm{FN}\mid }{\mathrm{TP}+\mathrm{FN}}$
Hausdorff distance	HD = max {supr ∈ ∂Rdm(s, r), sups ∈ ∂Sdm(r, s)}
Average symmetric surface distance, ASSD	$\mathrm{SD}=\frac{{\sum }_{\mathrm{s}\in \text{∂}\mathrm{S}}{\mathrm{d}}_{\mathrm{m}}\left(\mathrm{s},\text{∂}\mathrm{R}\right)+{\sum }_{\mathrm{s}\in \text{∂}\mathrm{R}}{\mathrm{d}}_{\mathrm{m}}\left(\mathrm{r},\text{∂}\mathrm{S}\right)}{\mid \text{∂}\mathrm{S}\mid +\mid \text{∂}\mathrm{R}\mid }$
Lesion-wise true positive rate, LTPR	$\text{LTPR}=\frac{\mathrm{TPL}}{\mathrm{TPL}+\mathrm{FNL}}$
Lesion-wise positive predictive value, LPPV	$\text{LPPV}=\frac{\mathrm{TPL}}{\mathrm{TPL}+\mathrm{FPL}}$