Algorithm 2 of the paper

[CharlesNord]

In the red circle shown above, why you divide N by 3 ?

N is the number of points, T(:, 4) has three elements, representing respectively the displacement in three dimensions of the coordinates.

If we take the first predicted displacement as Tx, and it's corresponding ground truth displacement as Tgx then, the resulting difference of reconstructed 3D shape should be: ||(Tx-Tgx, Tx-Tgx, Tx-Tgx, ... , Tx-Tgx)|| = |Tx-Tgx|*√(N)

Is there any mistake in my derivation above?

[cleardusk]

Thanks for your detailed reading, I check it out, you are right. It should be \sqrt{N}, not \sqrt{N/3}. I just made a writing mistake to take the dimension (3N) of the model base into account. The code is exactly \sqrt{N}, as https://github.com/cleardusk/3DDFA/blob/master/wpdc_loss.py#L82.

[cleardusk]

I checked again, it shoule be √(N/3) as the original version. The norm calculation should consider 3*N elements, not N elements. Specifically, the norm of the offset should be || 0,0,0,0, ..., 0,0,0,0, ..., Tx-Tgx,Tx-Tgx,Tx-Tgx,Tx-Tgx ...||.