Oriented object detection has been developed rapidly in the past few years, where rotation equivariant is crucial for detectors to predict rotated bounding boxes. It is expected that the prediction can maintain the corresponding rotation when objects rotate, but severe mutational in angular prediction is sometimes observed when objects rotate near the boundary angle, which is well-known boundary discontinuity problem. The problem has been long believed to be caused by the sharp loss increase at the angular boundary during training, and widely used IoU-like loss generally deal with this problem by loss-smoothing. However, we experimentally find that even state-of-the-art IoU-like methods do not actually solve the problem. On further analysis, we find the essential cause of the problem lies at discontinuous angular ground-truth(box), not just discontinuous loss. There always exists an irreparable gap between continuous model ouput and discontinuous angular ground-truth, so angular prediction near the breakpoints becomes highly unstable, which cannot be eliminated just by loss-smoothing in IoU-like methods. To thoroughly solve this problem, we propose a simple and effective Angle Correct Module (ACM) based on polar coordinate decomposition. ACM can be easily plugged into the workflow of oriented object detectors to repair angular prediction. It converts the smooth value of the model output into sawtooth angular value, and then IoU-like loss can fully release their potential. Extensive experiments on multiple datasets show that whether Gaussian-based or SkewIoU methods are improved to the same performance of AP50 and AP75 with the enhancement of ACM.

翻译：旋转目标检测在过去几年中发展迅速，其中旋转等变性对于检测器预测旋转边界框至关重要。期望当目标旋转时，预测结果能保持相应的旋转，但在边界角度附近目标旋转时，有时会观察到角度预测出现严重突变，这就是众所周知的边界不连续问题。长期以来，人们认为该问题是由训练过程中角度边界处的损失急剧增加所导致的，而广泛使用的IoU类损失通常通过损失平滑来处理这一问题。然而，我们通过实验发现，即使是最先进的IoU类方法实际上也并未解决该问题。进一步分析后，我们发现该问题的本质原因在于角度真值（边界框）的不连续性，而不仅仅是损失的不连续性。连续模型输出与不连续角度真值之间始终存在无法弥补的差距，因此断点附近的角度预测变得高度不稳定，仅通过IoU类方法中的损失平滑无法消除这一问题。为了彻底解决该问题，我们基于极坐标分解提出了一种简单有效的角度校正模块（ACM）。ACM可以轻松嵌入旋转目标检测器的工作流程中，用于修正角度预测。它将模型输出的平滑值转换为锯齿状角度值，从而使IoU类损失能够充分发挥其潜力。在多个数据集上的大量实验表明，无论是基于高斯的方法还是SkewIoU方法，在ACM的增强下，AP50和AP75的性能均得到提升且达到相同水平。