We focus on the construction of a loss function for the bounding box regression. The Intersection over Union (IoU) metric is improved to converge faster, to make the surface of the loss function smooth and continuous over the whole searched space, and to reach a more precise approximation of the labels. The main principle is adding a smoothing part to the original IoU, where the smoothing part is given by a linear space with values that increases from the ground truth bounding box to the border of the input image, and thus covers the whole spatial search space. We show the motivation and formalism behind this loss function and experimentally prove that it outperforms IoU, DIoU, CIoU, and SIoU by a large margin. We experimentally show that the proposed loss function is robust with respect to the noise in the dimension of ground truth bounding boxes. The reference implementation is available at gitlab.com/irafm-ai/smoothing-iou.

翻译：我们聚焦于边界框回归损失函数的构建。我们改进了交并比（Intersection over Union, IoU）度量，使其收敛速度更快、损失函数表面在整个搜索空间内平滑连续，并能更精确地逼近标签值。其主要原理是在原始IoU中引入平滑项，该项由从真实边界框到输入图像边缘呈线性递增的空间构成，从而覆盖整个空间搜索范围。我们阐明了该损失函数的动机与数学形式，并通过实验证明其性能大幅超越IoU、DIoU、CIoU和SIoU。实验结果表明，所提损失函数对真实边界框尺寸的噪声具有鲁棒性。参考实现代码位于gitlab.com/irafm-ai/smoothing-iou。