. 2021 Jul 1;11(7):629. doi: 10.3390/jpm11070629

Table 1.

Performance metrics applied to performance measurement of automatic segmentation of the mandible and the corresponding references and mathematical definitions. Note: $Y_{r}$ indicates the pixels in the reference standard (ground truth), and $Y_{p}$ is the pixels in the automatic segmentation. $| . |$ represents the number of voxels. $∥ . ∥$ represents the $L_{2}$ norm. a and b are corresponding points on the boundary of A and B.

Metric	Abbreviation	Definition
Overlap-based metrics, reported in percents (%)
Dice similarity index	Dice	$D i c e = \frac{2 \| Y_{r} \cap Y_{p} \|}{\| Y_{r} \| + \| Y_{p} \|} = \frac{2 T P}{2 T P + F P + F N}$
Sensitivity	Sen	$S e n = \frac{\| Y_{r} \cap Y_{p} \|}{\| Y_{r} \|} = \frac{T P}{T P + F N}$
Recall	Rec	$R e c a l l = S e n$
Positive Predictive Value	PVV	$P V V = \frac{\| Y_{r} \cap Y_{p} \|}{\| Y_{p} \|} = \frac{T P}{T P + F P}$
Jaccard similarity coefficient	Jac	$J a c = \frac{\| Y_{r} \cap Y_{p} \|}{\| Y_{r} \cup Y_{p} \|} = \frac{T P}{T P + F P + F N}$
Intersection over union	IoU	$I o U = J a c$
Specificity	Spe	$S p e c i f i c i t y = \frac{\| (1 - Y_{p}) \cap (1 - Y_{r}) \|}{\| Y_{p} \|} = \frac{T N}{T N + F P}$
False positive volume fraction	FPVF	$F P V F = \frac{\| Y_{p} - Y_{r} \|}{\| Y_{r} \|} = \frac{F P}{T P + F N}$
False negative volume fraction	FNVF	$F N V F = \frac{\| Y_{r} - Y_{p} \|}{\| Y_{r} \|} = \frac{F N}{T P + F N}$
Distance-based metrics, reported in millimeters (mm)
Average symmetric surface distance	ASD	$ASD (A, B) = \frac{d (A, B) + d (B, A)}{2},$ where $d (A, B) = \frac{1}{N} \sum_{a \in A} {min}_{b \in B} ∥ a - b ∥,$
Hausdorff distance	HD	$D_{HD} (A, B) = max (h (A, B), h (B, A)),$ where $h (A, B) = {max}_{a \in A} {min}_{b \in B} ∥ a - b ∥$
95th-percentile Hausdorff distance	95HD	$95 HD = max (h^{95 %} (A, B), h^{95 %} (B, A)),$ where $h^{95 %} (A, B) = {max}_{a \in A} {min}_{b \in B^{95 %}} ∥ a - b ∥$
Mean square error	MSE	$M S E = \frac{1}{n} \sum_{i = 1}^{n} {∥ A_{i} - B_{i} ∥}^{2}$ , where $A_{i}$ is the boundary of the i-th OAR and $B_{i}$ is the boundary of the i-th prediction.
Root mean square error	RMSE	$R M S E = \sqrt{M S E}$
Volume-based metrics, reported in percents (%)
Volume overlap error	VOE	$1 - \frac{\| Y_{r} \cap Y_{p} \|}{\| Y_{r} \cup Y_{p} \|}$
Volume error	VE	$V E = \frac{Y_{r} - Y_{p}}{Y_{r}} or \frac{Y_{p} - Y_{r}}{Y_{r}}$