Surface loss for medical image segmentation

Last decades have witnessed an unprecedented expansion of medical data in various largescale and complex systems. While achieving a lot of successes in many complex medical problems, there are still some challenges to deal with. Class imbalance is one of the common problems of medical image segmentation. It occurs mostly when there is a severely unequal class distribution, for instance, when the size of target foreground region is several orders of magnitude less that the background region size. In such problems, typical loss functions used for convolutional neural networks (CNN) segmentation fail to deliver good performances. Widely used losses,e.g., Dice or cross-entropy, are based on regional terms. They assume that all classes are equally distributed. Thus, they tend to favor the majority class and misclassify the target class. To address this issue, the main objective of this work is to build a boundary loss, a distance based measure on the space of contours and not regions. We argue that a boundary loss can mitigate the problems of regional losses via introducing a complementary distance-based information. Our loss is inspired by discrete (graph-based) optimization techniques for computing gradient flows of curve evolution. Following an integral approach for computing boundary variations, we express a non-symmetric L2 distance on the space of shapes as a regional integral, which avoids completely local differential computations. Our boundary loss is the sum of linear functions of the regional softmax probability outputs of the network. Therefore, it can easily be combined with standard regional losses and implemented with any existing deep network architecture for N-dimensional segmentation (N-D). Experiments were carried on three benchmark datasets corresponding to increasingly unbalanced segmentation problems: Multi modal brain tumor segmentation (BRATS17), the ischemic stroke lesion (ISLES) and white matter hyperintensities (WMH). Used in conjunction with the region-based generalized Dice loss (GDL), our boundary loss improves performance significantly compared to GDL alone, reaching up to 8% improvement in Dice score and 10% improvement in Hausdorff score. It also yielded a more stable learning process