  Average Hausdorff Distance (AVD) is a widely used performance measure to
calculate the distance between two point sets. In medical image segmentation,
AVD is used to compare ground truth images with segmentation results allowing
their ranking. We identified, however, a ranking bias of AVD making it less
suitable for segmentation ranking. To mitigate this bias, we present a modified
calculation of AVD that we have coined balanced AVD (bAVD). To simulate
segmentations for ranking, we manually created non-overlapping segmentation
errors common in cerebral vessel segmentation as our use-case. Adding the
created errors consecutively and randomly to the ground truth, we created sets
of simulated segmentations with increasing number of errors. Each set of
simulated segmentations was ranked using AVD and bAVD. We calculated the
Kendall-rank-correlation-coefficient between the segmentation ranking and the
number of errors in each simulated segmentation. The rankings produced by bAVD
had a significantly higher average correlation (0.969) than those of AVD
(0.847). In 200 total rankings, bAVD misranked 52 and AVD misranked 179
segmentations. Our proposed evaluation measure, bAVD, alleviates AVDs ranking
bias making it more suitable for rankings and quality assessment of
segmentations.
