  Automatic segmentation methods are an important advancement in medical
imaging analysis. Machine learning techniques, and deep neural networks in
particular, are the state-of-the-art for most automated medical image
segmentation tasks, ranging from the subcellular to the level of organ systems.
Issues with class imbalance pose a significant challenge irrespective of scale,
with organs, and especially with tumours, often occupying a considerably
smaller volume relative to the background. Loss functions used in the training
of segmentation algorithms differ in their robustness to class imbalance, with
cross entropy-based losses being more affected than Dice-based losses. In this
work, we first experiment with seven different Dice-based and cross
entropy-based loss functions on the publicly available Kidney Tumour
Segmentation 2019 (KiTS19) Computed Tomography dataset, and then further
evaluate the top three performing loss functions on the Brain Tumour
Segmentation 2020 (BraTS20) Magnetic Resonance Imaging dataset. Motivated by
the results of our study, we propose a Mixed Focal loss function, a new
compound loss function derived from modified variants of the Focal loss and
Focal Dice loss functions. We demonstrate that our proposed loss function is
associated with a better recall-precision balance, significantly outperforming
the other loss functions in both binary and multi-class image segmentation.
Importantly, the proposed Mixed Focal loss function is robust to significant
class imbalance. Furthermore, we showed the benefit of using compound losses
over their component losses, and the improvement provided by the focal variants
over other variants.
