We propose the Unified Focal loss, a new hierarchical framework that generalises Dice and cross entropy-based losses for handling class imbalance.

The most commonly used loss functions for segmentation are based on either the cross entropy loss, Dice loss or a combination of the two. Loss functions used in the training of deep learning algorithms differ in their robustness to class imbalance, with direct consequences for model convergence. Issues with class imbalance pose a significant challenge in medical datasets, with lesions often occupying a considerably smaller volume relative to the background. Machine learning techniques, and deep neural networks in particular, are the state-of-the-art for most medical image segmentation tasks. Electronic address: segmentation methods are an important advancement in medical image analysis. Electronic address: 4 Department of Radiology, University of Cambridge, Cambridge CB2 0QQ, United Kingdom Cancer Research UK Cambridge Centre, University of Cambridge, Cambridge CB2 0RE, United Kingdom Department of Information and Electrical Engineering and Applied Mathematics (DIEM), University of Salerno, Fisciano, SA 84084, Italy. Electronic address: 3 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom. Electronic address: 2 Department of Radiology, University of Cambridge, Cambridge CB2 0QQ, United Kingdom Cancer Research UK Cambridge Centre, University of Cambridge, Cambridge CB2 0RE, United Kingdom. 1 Department of Radiology, University of Cambridge, Cambridge CB2 0QQ, United Kingdom School of Clinical Medicine, University of Cambridge, Cambridge CB2 0SP, United Kingdom.

Crossentropy loss