Incorporating Boundary Uncertainty into loss functions for biomedical image segmentation

Manual segmentation is used as the gold-standard for evaluating neural networks on automated image segmentation tasks. Due to considerable heterogeneity in shapes, colours and textures, demarcating object boundaries is particularly difficult in biomedical images, resulting in significant inter and intra-rater variability. Approaches, such as soft labelling and distance penalty term, apply a global transformation to the ground truth, redefining the loss function with respect to uncertainty. However, global operations are computationally expensive, and neither approach accurately reflects the uncertainty underlying manual annotation. In this paper, we propose the Boundary Uncertainty, which uses morphological operations to restrict soft labelling to object boundaries, providing an appropriate representation of uncertainty in ground truth labels, and may be adapted to enable robust model training where systematic manual segmentation errors are present. We incorporate Boundary Uncertainty with the Dice loss, achieving consistently improved performance across three well-validated biomedical imaging datasets compared to soft labelling and distance-weighted penalty. Boundary Uncertainty not only more accurately reflects the segmentation process, but it is also efficient, robust to segmentation errors and exhibits better generalisation.