filter primitive subregion and feGaussianBlur

It seems unclear what the effect of the filter primitive subregion is on
feGaussianBlur (and other kernel-based primitives such as
feConvolutionMatrix). The 1.1 spec says
> All filter primitives have attributes *x*, *y*, *width* and *height* which
identify a subregion which restricts calculation and rendering of the given
filter primitive.

"Restricts calculation" is a bit ambiguous. Does this mean:
-- The implementation takes a snapshot of the input image, with the geometry
of the snapshot determined by the filter primitive subregion for the
feGaussianBlur, and performs processing on that, treating the boundaries of
the snapshot as the boundary where boundary conditions are applied.
or something else?

BTW the spec also says
> If the input has infinite extent and is a tile, the filter is evaluated
with periodic boundary conditions.

I'm not sure what it means for the input to have infinite extent in this
context, and I'm not sure what it means to be "a tile". Does it mean that
the input is an feTile? Could this be more precisely defined?

Rob
-- 
"He was pierced for our transgressions, he was crushed for our iniquities;
the punishment that brought us peace was upon him, and by his wounds we are
healed. We all, like sheep, have gone astray, each of us has turned to his
own way; and the LORD has laid on him the iniquity of us all." [Isaiah
53:5-6]