Anatomical and Diagnostic Bayesian Segmentation in Prostate MRI $-$Should Different Clinical Objectives Mandate Different Loss Functions?

We hypothesize that probabilistic voxel-level classification of anatomy and malignancy in prostate MRI, although typically posed as near-identical segmentation tasks via U-Nets, require different loss functions for optimal performance due to inherent differences in their clinical objectives. We investigate distribution, region and boundary-based loss functions for both tasks across 200 patient exams from the publicly-available ProstateX dataset. For evaluation, we conduct a thorough comparative analysis of model predictions and calibration, measured with respect to multi-class volume segmentation of the prostate anatomy (whole-gland, transitional zone, peripheral zone), as well as, patient-level diagnosis and lesion-level detection of clinically significant prostate cancer. Notably, we find that distribution-based loss functions (in particular, focal loss) are well-suited for diagnostic or panoptic segmentation tasks such as lesion detection, primarily due to their implicit property of inducing better calibration. Meanwhile, (with the exception of focal loss) both distribution and region/boundary-based loss functions perform equally well for anatomical or semantic segmentation tasks, such as quantification of organ shape, size and boundaries.