Table 5 Summary of Evaluation Metrics for Vascular Segmentation: TP = True Positive, TN = True Negative, FP = False Positive, FN = False Negative, \(V_p\) = Predicted Volume, \(V_g\) = Ground Truth Volume, A, B = Sets of Points for Spatial Distance, \(T_{\text {prec}}\) = Topological Precision, \(T_{\text {sens}}\) = Topological Sensitivity, RI = Rand Index, x = Predicted Segmentation Value, y = Ground Truth Value, p(x, y) = Joint Probability Distribution of x and y, p(x) = Marginal Probability Distribution of x, p(y) = Marginal Probability Distribution of y, TPR = True Positive Rate, FPR = False Positive Rate, d(FPR) = Differential of the False Positive Rate.

Overlap-based

Dice Similarity Coefficient (DSC)

\(DSC = \frac{2TP}{FP + FN + 2TP}\)¹²³

Easy to implement - widely used (26/31 studies). Good for overlap assessment.

Sensitive to class imbalance and lacks connectivity assessment.

Sensitivity (Recall or TPR)

\(Sensitivity = \frac{TP}{TP + FN}\)¹²⁴

Measures true positive rates.

Ignores structural/topological features.

Specificity (TNR)

\(Specificity = \frac{TN}{FP + TN}\)¹²⁴

Measures true negative rates.

Ignores structural/topological features.

Precision

\(Precision = \frac{TP}{TP + FP}\)¹²⁴

Accounts for false positives/negatives.

Rarely used in medical image segmentation.

F1-Score

\(F1 = 2 \cdot \frac{\text {Precision} \cdot \text {Recall}}{\text {Precision} + \text {Recall}}\)¹²⁴

Balances precision and recall.

Rarely used in medical image segmentation.

Topology-preserving

Centerline Dice (clDice)

\(clDice = \frac{2T_{\text {prec}}T_{\text {sens}}}{T_{\text {prec}} + T_{\text {sens}}}\)¹²⁵

Preserves connectivity of thin, tubular structures like vessels.

Computationally expensive - less commonly used (2/31 studies).

Volume-based

Relative Volume Difference (RVD)

\(RVD = \frac{|V_p - V_g|}{V_g}\)¹²³

Quantifies the disparity in volume.

Sensitive to small structures

Spatial distance-based

95th Percentile Hausdorff Distance (95HD)

percentile(h(A, B), 95)¹²⁶

Captures boundary accuracy.

Sensitive to outliers or small discrepancies.

Average Symmetric Surface Distance (ASSD)

\(ASSD = \frac{1}{2} \left( \frac{1}{|A|} \sum _{a \in A} \min _{b \in B} d(a,b) + \frac{1}{|B|} \sum _{b \in B} \min _{a \in A} d(b,a) \right)\)¹²⁷

Provides average boundary accuracy.

Less sensitive to topology, focuses on boundary alignment.

Probabilistic-based

Area Under the Curve (AUC)

\(AUC = \int _0^1 TPR(FPR) \, d(FPR)\)¹²⁸

Common in binary classification models, reflects overall performance.

Rarely used (3/31 studies).

Pair-counting-based

Adjusted Rand Index (ARI)

\(ARI = \frac{\text {RI} - \text {Expected\_RI}}{\text {Max\_RI} - \text {Expected\_RI}}\)¹²⁸

Adjusts for chance in clustering assessments.

Not widely used in vascular segmentation.

Information-theoretic

Mutual Information (MI)

\(MI(X,Y) = \sum _{x \in X} \sum _{y \in Y} p(x,y) \log \left( \frac{p(x,y)}{p(x)p(y)} \right)\)¹²⁸

Captures shared info between segmented and true data.

Complex to compute and rarely used in vascular segmentation.