Can you explain a little bit more about the matting loss?

[yuhaoliu7456]

In "Matting Laplacian [22] may result in blurry images when it is used with another network like one with an encoder-decoder architecture. But it does not have this issue in CAP-VSTNet, since the bijective transformation of reversible network theoretically requires all information to be preserved."

I'm curious about the relationship between the bijective transformation of a reversible network that theoretically needs to preserve all information and the image blur caused by Laplacian matting? Even after reading this paragraph several times, I still cannot fully understand your point here.

So can you please kindly help me figure this out?

Thanks.

[linfengWen98]

1.Network
Given input $X$ and $X_{smooth}$ , we have,
$\quad Net.Forward (X) \rightarrow Y$ ,
$\quad Net.Forward (X_{smooth}) \rightarrow Y_{smooth}$ .
For reversible network, $Y \neq Y_{smooth}$ when $X \neq X_{smooth}$ .
For encoder, it's possible that $Enc(X) = Enc(X_{smooth}) = Y_{smooth}$ .

Similarly,
$\quad Net.Backward (Y) \rightarrow X$ ,
$\quad Net.Backward (Y_{smooth}) \rightarrow X_{smooth}$ .
For reversible network, $X \neq X_{smooth}$ when $Y \neq Y_{smooth}$ .
For decoder, it's possible that $Dec(Y) = Dec(Y_{smooth}) = X_{smooth}$ .

2.Linear Transform
Assuming the feature $Y$ and $Y_{smooth}$ have the same content factor $C$ , we have,
$\quad L*C \rightarrow Y$ ,
$\quad L_{smooth}*C \rightarrow Y_{smooth}$ .

The stylized result depends on $L$ and covariance matrix $\Sigma$ ($\Sigma=L*L^T$).