  Dice similarity coefficient (DSC) and Hausdorff distance (HD) are widely used
for evaluating medical image segmentation. They have also been criticised, when
reported alone, for their unclear or even misleading clinical interpretation.
DSCs may also differ substantially from HDs, due to boundary smoothness or
multiple regions of interest (ROIs) within a subject. More importantly, either
metric can also have a nonlinear, non-monotonic relationship with outcomes
based on Type 1 and 2 errors, designed for specific clinical decisions that use
the resulting segmentation. Whilst cases causing disagreement between these
metrics are not difficult to postulate. This work first proposes a new
asymmetric detection metric, adapting those used in object detection, for
planning prostate cancer procedures. The lesion-level metrics is then compared
with the voxel-level DSC and HD, whereas a 3D UNet is used for segmenting
lesions from multiparametric MR (mpMR) images. Based on experimental results we
report pairwise agreement and correlation 1) between DSC and HD, and 2) between
voxel-level DSC and recall-controlled precision at lesion-level, with Cohen's
[0.49, 0.61] and Pearson's [0.66, 0.76] (p-values}<0.001) at varying cut-offs.
However, the differences in false-positives and false-negatives, between the
actual errors and the perceived counterparts if DSC is used, can be as high as
152 and 154, respectively, out of the 357 test set lesions. We therefore
carefully conclude that, despite of the significant correlations, voxel-level
metrics such as DSC can misrepresent lesion-level detection accuracy for
evaluating localisation of multifocal prostate cancer and should be interpreted
with caution.
