  The Dice similarity coefficient (DSC) is both a widely used metric and loss
function for biomedical image segmentation due to its robustness to class
imbalance. However, it is well known that the DSC loss is poorly calibrated,
resulting in overconfident predictions that cannot be usefully interpreted in
biomedical and clinical practice. Performance is often the only metric used to
evaluate segmentations produced by deep neural networks, and calibration is
often neglected. However, calibration is important for translation into
biomedical and clinical practice, providing crucial contextual information to
model predictions for interpretation by scientists and clinicians. In this
study, we provide a simple yet effective extension of the DSC loss, named the
DSC++ loss, that selectively modulates the penalty associated with
overconfident, incorrect predictions. As a standalone loss function, the DSC++
loss achieves significantly improved calibration over the conventional DSC loss
across six well-validated open-source biomedical imaging datasets, including
both 2D binary and 3D multi-class segmentation tasks. Similarly, we observe
significantly improved calibration when integrating the DSC++ loss into four
DSC-based loss functions. Finally, we use softmax thresholding to illustrate
that well calibrated outputs enable tailoring of recall-precision bias, which
is an important post-processing technique to adapt the model predictions to
suit the biomedical or clinical task. The DSC++ loss overcomes the major
limitation of the DSC loss, providing a suitable loss function for training
deep learning segmentation models for use in biomedical and clinical practice.
Source code is available at: https://github.com/mlyg/DicePlusPlus.
