Loss definition: from the paper to the implementation

[ReubenDo]

Hello,

First I would like to say that I really enjoyed your work. Congrats!
I have a simple question regarding the denseCRF loss. I do not understand how your implementation works. Why is it a simple dot product? I am probably missing what AS is in your code.

rloss/pytorch/pytorch-deeplab_v3_plus/DenseCRFLoss.py

Line 34 in 1caa759

densecrf_loss -= np.dot(segmentations, AS)

Thanks a lot,
Reuben

[ReubenDo]

Does it in fact correspond to the formula in the appendix?

[mkusner]

+1 I have the same question!

[mkusner]

Oh actually it looks like #3 talks about this. Is it right @meng-tang that the loss is:

Or did I miss something?

[meng-tang]

Yes, it corresponds to the formula. Sorry for inconsistent notations. A or w denotes the affinity matrix. S or X means the segmentation variable. AS is the result of the product of affinity matrix and segmentation.

Note that for dense CRF, we don't explicitly save A in our implementation. However, one can compute AS efficiently with fast Bilateral filtering.