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Table 3 Pair counting cardinalities versus overlap cardinalities in examples. Five examples show that the pair counting cardinalities (a, b, c, and d) cannot be used in place of the overlap cardinalities (TP, FP, FN, and TN) to calculate the Jaccard index, as it is commonly used in the literature

From: Metrics for evaluating 3D medical image segmentation: analysis, selection, and tool

P1 P2 TP FP FN TN J A C 1 a b c d J A C 2
1,0,1,1 1,1,0,0 1 2 1 0 0.25 1 2 1 2 0.25
1,1,1,1 0,0,0,1 1 3 0 0 0.25 3 3 0 0 0.5
0,1,0,1 1,1,0,0 1 1 1 1 0.33 0 2 2 2 0.0
0,0,0,0 0,0,0,1 0 0 1 3 0.0 3 0 3 0 0.5
1,0,0,1 1,1,0,1 2 0 1 1 0.67 1 2 1 2 0.25