The formulation of training regression targets in FCOS paper

[geoexploring]

Hi, thank you all for making FCOS available!

Two things in the FCOS paper confuse me：

1. As shown in the figure below, is there a comma missing in the red line? I found this in both the conference edition and the journal edition of FCOS paper.
   

2. As the FCOS paper says,
   
   and, the training regression targets for the location is formulated as:
   
   However, when I read the FCOS code, I found it was not the same as the definition in the paper，
   

   AdelaiDet/adet/utils/comm.py

   Line 54 in c07ba9a

   locations = torch.stack((shift_x, shift_y), dim=1) + stride // 2

   
   

   AdelaiDet/adet/modeling/fcos/fcos_outputs.py

   Line 191 in c07ba9a

   xs, ys = locations[:, 0], locations[:, 1]

   
   

   AdelaiDet/adet/modeling/fcos/fcos_outputs.py

   Line 208 in c07ba9a

   l = xs[:, None] - bboxes[:, 0][None]

   
   The definition in the code feels more like the following formula：
   

Please correct me if I made any mistakes.
Thank you in advance

[tianzhi0549]

@geoexploring 1) Thank you for pointing it out. You are right. We miss a comma here. 2) The implementation is consistent with our paper. locations are x and y in Eq (1).

[geoexploring]

@tianzhi0549 Thank you for your reply!

To 2), my understanding is,

• location (x,y) is in the coordinate system of the feature map, which can be mapped to the coordinate system of the input image and can be expressed as：
  
• and the Bi is the gt bbox's definition, which is also in the coordinate system of the input image.
  

I feel that Eq (1) is subtracting the numbers from two different coordinate systems.

Please correct me if I made any mistakes.
Thank you in advance

[tianzhi0549]

@geoexploring It seems you are right ... We mix up the two coordinate systems here. Sorry about that. We will fix it in a revision.

[geoexploring]

@tianzhi0549 hahaha, thank you for your honesty! many thanks!