GIoU Loss 损失函数浅析

GIoU Loss

参考文献：Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression

GIoU是源自IoU的一种边框预测的损失计算方法，在目标检测等领域，需要对预测边框（pre BBox）与实际标注边框（ground truth BBox）进行对比，计算损失。在Yolo算法中，给定预测值与ground truth的 x\y\w\h 进行预测，采用回归损失。但实际上，回归损失并不是该问题的最好损失函数，因为其只关注 x\y\w\w 对应的“距离”，而本质上我们想要得到 IoU 值比较大的预测框，两者联系并不大。那么为什么不直接采用IoU值作为损失函数呢？ 因为一旦预测框与真实框不相交，那么IoU都为0，也就是说，在很大的范围内（不相交的区域），损失函数是没有梯度的，因此才有了GIoU Loss（Generalized Intersection over Union）。

1 为什么基于距离的损失函数不行？

如上图所示，在基于L1和L2范数的度量下，距离相同的两个框框，实际IoU值可能相差很远，所以说，这类损失函数在预测边界框时并不是一个好的选择！

2 GIoU的定义

其中：C代表包围A、B的最小体积（或面积），A、B是啥形状，C就是啥形状，你懂的； |C(A U B)| 为 C - (A U B)

性质：

 	1) 当IoU值为1时，GIoU 为 1，即|A U B| = |A ∩ B|；
	2) Iou为0时，GIoU<=0;
	3) -1<= GIoU <=1;
	4) GIou <= IoU;

英文原文：For two arbitrary convex shapes (volumes) A, B ⊆ S ∈Rⁿ, we first find the smallest convex shapes C ⊆ S ∈ Rⁿenclosing both A and B. For comparing two specific types of geometric shapes, C can be from the same type. For
example, two arbitrary ellipsoids, C could be the smallest ellipsoids enclosing them. Then we calculate a ratio between the volume (area) occupied by C excluding A and B and divide by the total volume (area) occupied by C. This represents a normalized measure that focuses on the empty volume (area) between A and B. Finally GIoU is attained by subtracting this ratio from the IoU value.

1. Similar to IoU, GIoU as a distance, e.g. LGIoU = 1 − GIoU, holding all properties of a metric such as non-negativity, identity of indiscernibles, symmetry and triangle inequality.
2. Similar to IoU, GIoU is invariant to the scale of the problem.
3. GIoU is always a lower bound for IoU, i.e. ∀A, B ⊆ S GIoU(A, B) ≤ IoU(A, B), and this lower bound becomes tighter when A and B have a stronger shape

GIoU作为损失函数

可见计算GIoU损失的方式其实就是计算GIoU，只不过最终结果返回的时1-GIoU。这是因为1-GIoU的取值范围在[0,2]上，且有一定的“距离”性质，即两个框重叠区域越大，损失越小，反之越大。

写在最后：

本文是对作者原文的总结，如有疑问，欢迎讨论。