# Meaning of topological distance between 2 pixels

I came across the notion of topology and topological distance in the context of image processing several times (especially when it came to mathematical morphology). I looked for a not too abstract explanation of "topological distance" but haven't found one yet. Can you please explain (in layaman's terms) the notion of topological distance between 2 pixels? And what's the difference between a euclidean distance and a topological distance in image-processing?

• Can you give us some context, e.g., a citation to the source where you saw the phrase used and the surrounding context?
– D.W.
Feb 22, 2016 at 21:01

This defines a graph (two pixels are connected by an edge if they are neighbors). The topological distance between two pixels $p,q$ is then the graph distance between $p$ and $q$.
The first choice above corresponds to $L^1$ ("Manhattan") distance, and the second choice to $L^\infty$ distance. This contrasts with the usual $L^2$ (Euclidean) distance.