CRF message passing as convolution operation
I read the article. The meaning of the equation:
$$[G\otimes Q](f_i)$$ stand for $G$ convolution with $Q$ in the feature point $f_i$ and not multiplied by $f_i$. 

The $f_j$ is hidden inside the convolution operation. 

The actual operation is done using cross bilateral filter.
You can see more information on the Project site of the article.
You can also find a source code in this site.