. 2021 Mar 12;21(6):2027. doi: 10.3390/s21062027

Table 2.

Performance measures for liver vessel segmentation methods (S), in relation to the reference (R), based on thirty one studies in this review, where true positives ( $T P$ ) are pixels classified correctly as positive, false positives ( $F P$ ) are pixels classified incorrectly as positive, true negatives ( $T N$ ) are pixels classified correctly as not positive, false negatives ( $F N$ ) are pixels classified incorrectly as not positive. For contours marked R and S: r and s represent points belonging to the corresponding contours, while $d_{s}$ and $d_{r}$ are the distances from points s and r to the nearest points of the R and S contours.

Metrics	Standard Formula	Description
Sensitivity (Sens); recall; true positive rate (TPR) [42]	$T P R = S e n s = \frac{T P}{T P + F N}$	Proportion of positives that are correctly identified.
Accuracy (Ac) [43]	$A c = \frac{T P + T N}{T P + T N + F P + F N}$	Proportion of detected true samples that are actually true.
Specificity (Spec) [42]	$S p e c = \frac{T N}{T N + F P}$	Proportion of negatives that are correctly identified.
Precision; positive predictive value (PPV) [44]	$P P V = \frac{T P}{T P + F P}$	Proportion of positive results that are true positives.
Negative predictive value (NPV) [44]	$N P V = \frac{T N}{T N + F P}$	Proportion of negative results that are true negatives.
False positive rate (FPR) [45]	$F P R = 1 - S p e c$	Ratio of the number of negative samples wrongly categorized as positive ( $F P$ ) to the total number of actual negative samples.
False negative rate (FNR) [45]	$F N R = 1 - T P R$	Ratio of the number of positive samples wrongly categorized as negative ( $F N$ ) to the total number of actual positive samples.
Dice similarity coefficient (DSC) [46]	$D S C = \frac{2 \cdot T P}{F P + F N + 2 \cdot T P}$	Similarity between two sample sets.
Jaccard similarity coefficient (JSC) [47]	$J S C = \frac{T P}{F P + F N + T P}$	Similarity between finite sample sets.
Volumetric overlap error (VOE) [48]	$V O E = 1 - J S C$	The $V O E$ indicates segmentation performance; if the $V O E$ is close to 0, this represents a perfect segmentation.
Distance error ( $e_{D}$ ) [49]	$e_{D} = \frac{1}{\| S \|} (\sum_{s = 1}^{\| S \|} \| d_{s} \|)$	Measure of the average distance calculated from all s points on S to the closest point on R.
Symmetric distance error ( $e_{D s y m}$ ) [50]	$e_{D s y m} = \frac{1}{\| S \| + \| R \|} (\sum_{s = 1}^{\| S \|} \| d_{s} \| + \sum_{r = 1}^{\| R \|} \| d_{r} \|)$	Measure of the average distance calculated from all s points on S to the closest point on R and vice versa.
Root mean standard error (RMSE) [49]	$R M S E = \sqrt{\frac{1}{\| S \|} (\sum_{s = 1}^{\| S \|} \| d_{s} \|)}$	Measure of the average squared difference between the estimated values and the actual value.
Root mean squared symmetric surface distance (RMSD) [51]	$R M S D = \sqrt{\frac{1}{\| S \| + \| R \|}} \times \sqrt{\sum_{x \in S} d^{2} (x, R) + \sum_{y \in R} d^{2} (y, S)}$	The $R M S D$ indicates the segmentation performance between two contours S and R; the lower the $R M S D$ , the better the segmentation result.
Hausdorff distance (HD) [52]	$H D = max ({max}_{s \in S} \| d_{s} \|, {max}_{r \in R} \| d_{r} \|)$	Overlapping index, which measures the largest Euclidean distance between two contours S and R and vice versa, computed over all pixels of each curve.
Classification error ( $ϵ$ ) [18]	$ϵ = \| B_{e} \| / \| B \|$	Proportion of the incorrectly classified vessel branches $\| B_{e} \|$ to all vessel branches $\| B \|$ .
Recognition rate (RR) [19]	$R R = \| B_{t} \| / \| B \|$	Proportion of the correctly classified vessel branches $\| B_{t} \|$ to all vessel branches $\| B \|$ .