edges vs slopes in digitised signals? Philosophic

I's doing some image processing.

Has anyone seen any good philosophical discussions
on the distinctions between 'edges and slopes'
within a region of interest?

As one 'zooms' into an image what used to be an
'edge'd starts to look like a slope [and it is even
worse when done in reverse because you know it was a
local slope and now it looks like an edge..]

Some times it gets confused between optical blur,
image digitisation, or object range as the source of
an effect.

Philip Oakley