Widely used loss functions for CNN segmentation, e.g., Dice or cross-entropy,
are based on integrals over the segmentation regions. Unfortunately, for highly
unbalanced segmentations, such regional summations have values that differ by
several orders of magnitude across classes, which affects training performance
and stability. We propose a boundary loss, which takes the form of a distance
metric on the space of contours, not regions. This can mitigate the
difficulties of highly unbalanced problems because it uses integrals over the
interface between regions instead of unbalanced integrals over the regions.
Furthermore, a boundary loss complements regional information. Inspired by
graph-based optimization techniques for computing active-contour flows, we
express a non-symmetric $L_2$ distance on the space of contours as a regional
integral, which avoids completely local differential computations involving
contour points. This yields a boundary loss expressed with the regional softmax
probability outputs of the network, which can be easily combined with standard
regional losses and implemented with any existing deep network architecture for
N-D segmentation. We report comprehensive evaluations and comparisons on
different unbalanced problems, showing that our boundary loss can yield
significant increases in performances while improving training stability. Our
code is publicly available: this https URL .

基于轮廓空间的边界损失可弥补高度不平衡问题，结合标准区域损失，实现 N 维分割的深度网络架构，显著提高训练稳定性。