Bbox regression loss function in target detection -l2, smooth L1, IOU, giou, Diou, ciou, focal eiou, alpha IOU, Siou

Two tasks of target detection , Classification and location regression , This post summarizes the classic position regression loss function as follows , In chronological order of publication .

L1、L2、smooth L1 loss

Put forward smooth L1 loss The paper of ：

L1 The lowest point is not differentiable , So it will not converge to the lowest point , May oscillate near the optimal solution . and L2 Loss is easy to cause gradient explosion at outliers .smooth L1 It combines the advantages of both .

IoU loss

Put forward IoU loss The paper of ：

Whether it's L2 still smooth L1 loss Did not consider The relevance of the four points and Scale invariance , This is a fatal shortcoming , When two pairs of prediction boxes and GT Framed IoU Phase at the same time , The pair with larger scale loss It will be higher , Or as shown in the figure below , Use the lower left corner and upper right corner to calculate the loss ,L2 loss identical , but IoU But not the same .

IoU There are two forms of loss , The latter is more commonly used ：
$L_{IoU}=-lnIoU$
$L_{IoU}=1-IoU$
such ,BBox The evaluation index and optimization index of regression problem have been overlapped and unified .

GIoU loss

Put forward GIoU loss The paper of ：

IoU loss The biggest drawback is when the two boxes do not intersect IoU Horizontal 0, Loss constant 1, There is no way to provide optimized gradients .
Here's the picture ( The picture is from CHEN), On the right loss It should be smaller , but IoU loss It's the same .

GIoU A concept of minimum closure region is introduced , That is, the smallest rectangular box that can wrap the prediction box and the real box , among ,$A_c$ Is the minimum closure area ,$u$ It is the union of prediction box and real box , that GIoU The molecule of the second term is the white area in the above figure , The higher the value of the white area than the minimum closure area ,loss The higher the .

DIoU loss

and
In the above figure, there are three cases IoU and GIoU Of loss Are all 0.75, But obviously, the third case should be a better prediction , and DIoU loss These situations can be expressed more accurately , The calculation formula is as follows , comparison IoU Loss of one more penalty , yes
$[\frac{twoindividualboxinheartspotOfotypedistanceleave}{mostSmallclosepackageMomentshapeYeshornLineLongdegree}{]}^2$

DIoU There are also the following advantages ：

• because DIoU Directly minimize the distance between the two boxes , So convergence is better than GIoU Much faster , As shown in the figure below . Especially when the relative direction of the two boxes is vertical or horizontal .
• As NMS Better results can be obtained when evaluating indicators .
  

CIoU loss（Complete IoU Loss）

And DIoU loss From the same article
The author thinks that , well IoU Loss should consider three factors ：

1. The area of intersection
2. Distance from the center
3. Aspect ratio

and IoU and GIoU loss Only the first factor is considered ,DIoU loss Consider the second factor more .
The author also puts forward CIoU loss, It can measure the coincidence degree and similarity of two boxes more accurately , Than DIoU There is an additional penalty item of aspect ratio $v$,$\alpha$ It's the equilibrium coefficient .


The author shows through experiments that ,CIoU Compared to other IoU Loss achieved better experimental results .

Focal-EIoU loss

I can see that the comments on this loss are not very good , I haven't looked carefully yet , Dig a hole .

Alpha IoU

Simply put, yes IoU loss The family did a power operation , The formula shown in the figure below .

Pictured above ,alpha-IoU It can be improved adaptively IoU Object loss and gradient to improve BBox Regression accuracy , And for small data sets and noise BBox Provides better robustness .

SIoU loss

5 The hot month is still the new loss of preprint , But the effect is better than CIoU A lot of improvement , Dig a hole .