Dice Coefficient and Segmentation Metrics

For a predicted region A and reference region B, Dice is twice the size of their intersection divided by the sum of their sizes. For binary masks it is 2TP divided by 2TP plus FP plus FN. A score of one indicates identical nonempty masks, while zero indicates no overlap. Dice emphasizes overlap and is related to the Jaccard index, also called intersection over union: Dice equals twice IoU divided by one plus IoU. Overlap is only one aspect of segmentation quality. Two masks can achieve similar Dice while having different boundary errors, particularly when the target is large and a small contour shift affects relatively few pixels. Hausdorff distance measures the largest nearest-boundary separation between the two contours, making it sensitive to a single distant error. Variants such as a percentile Hausdorff distance reduce that sensitivity by using a high quantile, but must be named precisely. Aggregation matters. Per-case averaging weights cases equally. Pooling weights cases by their Dice denominators, 2TP plus FP plus FN, so large foreground regions or error counts can dominate. In multiclass tasks, macro, micro, weighted, and per-class summaries can tell different stories. Background can dominate pixel counts, so clarify whether it is included. Empty reference or prediction masks also need a documented convention because the formula may be undefined when both are empty. Class imbalance does not disappear just because Dice focuses on overlap. A tiny missed lesion can matter greatly to a clinician while contributing little to a global dataset score. Report per-case and per-class behavior, and select complementary metrics based on the intended use. Boundary distances should account for voxel spacing and coordinate units; otherwise a voxel error has different physical meaning across scans. Metrics compare masks; they do not establish clinical correctness or utility. Define the annotation protocol, threshold or discretization rule, and evaluation unit. For consequential uses, review representative failures and discuss clinically meaningful tolerances with domain experts.