Semantic segmentation (SS) is an important perception manner for self-driving cars and robotics, which classifies each pixel into a pre-determined class. The widely-used cross entropy (CE) loss-based deep networks has achieved significant progress w.r.t. the mean Intersection-over Union (mIoU). However, the cross entropy loss can not take the different importance of each class in an self-driving system into account. For example, pedestrians in the image should be much more important than the surrounding buildings when make a decisions in the driving, so their segmentation results are expected to be as accurate as possible. In this paper, we propose to incorporate the importance-aware inter-class correlation in a Wasserstein training framework by configuring its ground distance matrix. The ground distance matrix can be pre-defined following a priori in a specific task, and the previous importance-ignored methods can be the particular cases. From an optimization perspective, we also extend our ground metric to a linear, convex or concave increasing function $w.r.t.$ pre-defined ground distance. We evaluate our method on CamVid and Cityscapes datasets with different backbones (SegNet, ENet, FCN and Deeplab) in a plug and play fashion. In our extenssive experiments, Wasserstein loss demonstrates superior segmentation performance on the predefined critical classes for safe-driving.
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