Boundary-wise loss for medical image segmentation based on fuzzy rough sets

The loss function plays an important role in deep learning models as it determines the model convergence behavior and performance. In semantic segmentation, many methods utilize pixel-wise (e.g. cross-entropy) and region-wise (e.g. dice) losses while boundary-wise loss is underexplored. It is known that one of the key aims of semantic segmentation is to precisely delineate objects' boundaries. Hence, it is essential to design a loss function that measures the errors around objects' boundaries. Fuzzy rough sets are constituted by the fuzzy equivalence relation, which is commonly used to measure the difference between two sets. In this paper, the lower approximation of fuzzy rough sets is proposed to construct the boundary-wise loss in deep learning models for the first time. The experiments with various segmentation models and datasets have verified that the proposed fuzzy rough sets loss is superior to other boundary-wise losses in terms of segmentation accuracy and time complexity. Compared with the commonly used pixel-wise and region-wise losses, the proposed boundary-wise loss performs similarly in dice coefficient, pixel-wise accuracy, but has a better performance in Hausdorff distance and symmetric surface distance. It indicates that the proposed loss provides a better guidance for segmentation models in producing more accurate shapes of the target objects. Code is available online at Github: https://github.com/qiaolin1992/Boundary-Loss.