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?

  • 1
    $\begingroup$ Can you give us some context, e.g., a citation to the source where you saw the phrase used and the surrounding context? $\endgroup$
    – D.W.
    Feb 22, 2016 at 21:01

1 Answer 1


Nonlinear Signal and Image Processing: Theory, Methods, and Applications defines topological distance as follows. First, you have to define when two pixels are neighbors. The book offers two possibilities:

  • The neighbors of a pixel are the 4 "cardinal" pixels around it.
  • The neighbors of a pixel are the 8 pixels surrounding it.

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.