Oriented bounding box regression is crucial for oriented object detection. However, regression-based methods often suffer from boundary problems and the inconsistency between loss and evaluation metrics. In this paper, a modulated Kalman IoU loss of approximate SkewIoU is proposed, named MKIoU. To avoid boundary problems, we convert the oriented bounding box to Gaussian distribution, then use the Kalman filter to approximate the intersection area. However, there exists significant difference between the calculated and actual intersection areas. Thus, we propose a modulation factor to adjust the sensitivity of angle deviation and width-height offset to loss variation, making the loss more consistent with the evaluation metric. Furthermore, the Gaussian modeling method avoids the boundary problem but causes the angle confusion of square objects simultaneously. Thus, the Gaussian Angle Loss (GA Loss) is presented to solve this problem by adding a corrected loss for square targets. The proposed GA Loss can be easily extended to other Gaussian-based methods. Experiments on three publicly available aerial image datasets, DOTA, UCAS-AOD, and HRSC2016, show the effectiveness of the proposed method.

翻译：定向捆绑框回归对于定向天体探测至关重要。 但是,基于回归的方法往往存在边界问题,而且损失和评价指标之间也存在不一致之处。 本文建议采用调制的Kalman IoU损失近似SkewIoU, 名为MKIoU。 为避免边界问题,我们将定向捆绑框转换为高山分布,然后使用卡尔曼过滤器来估计交叉区域。然而,计算得出的与实际交叉区域之间存在很大差异。因此,我们提议采用一个调制因子来调整角度偏差的敏感度和宽度偏差抵消与损失差异的偏差,使损失与评估标准更加一致。此外,高斯模型方法避免了边界问题,但同时造成方形物体的角混淆。 因此,高斯安格尔损失(GA Loss) 是为了通过增加平方目标的更正损失来解决这一问题的。 拟议的GA损失可以很容易扩大到其他高斯方法。 在三种公开提供的空中图像集、 DOTA、 UCAS-AOD和HRSC2016上进行的实验显示了拟议方法的有效性。