0
$\begingroup$

I'm a computer vision PhD student, and I'm looking for an efficient approximation to the following problem, which could end up helping in image to image matching. Failing that, pointers to relevant literature would be nice.

Say we have two directed graphs $G_1 := (V_1, E_1)$ and $G_2 := (V_2, E_2)$. Let $(G \times G)'$ be the set of pairs of graphs which are topologically isomorphic. Finally, let $\text{Sim}: (G \times G)' \to \mathbb{R}$ be a measure of similarity between two topologically isomorphic graphs. For example, in a computer vision setting we might define $\text{Sim}$ as the sum of the similarities of the corresponding edges in the graphs, where the edge-based similarities could come from a comparison of underlying pixels.

I would like to efficiently (perhaps approximately) find $$ \max_{g_1 \subseteq G_1, g_2 \subseteq G_2, (g_1, g_2) \in (G, G)'} \text{Sim}(g_1, g_2). $$

In words, I want to find isometric subgraphs of $G_1$ and $G_2$ with the highest similarity.

Extra credit: If this is hard for general similarity functions $\text{Sim}$, but easy for certain constructions of $\text{Sim}$, please let me know.

$\endgroup$
4
  • $\begingroup$ Dear emchristiansen, your question is really interesting! But the picture in your profile is rather horrific! May I ask you to change it please? $\endgroup$
    – user42090
    Nov 6, 2013 at 13:01
  • 1
    $\begingroup$ I like it! It's a photo from an early experiment in contact lens displays; in this photo the display is being tested on a rabbit. $\endgroup$ Nov 6, 2013 at 19:17
  • 1
    $\begingroup$ There is no problem about the photo. Poor rabbit! :-( $\endgroup$
    – user42090
    Nov 7, 2013 at 1:49
  • 4
    $\begingroup$ I just saw this image. Why someone would adopt a picture of animal cruelty as their emblem is a mystery to me. $\endgroup$ Dec 29, 2013 at 6:34

1 Answer 1

-1
$\begingroup$

Well, if you are interested in graph matching algorithms that are really cool, have a look at "Mohammad Shafkat Amin, Russell L. Finley Jr., Hasan M. Jamil: Top-k Similar Graph Matching Using TraM in Biological Networks. IEEE/ACM Trans. Comput. Biology Bioinform. 9(6): 1790-1804 (2012)". :) More importantly, there are better algorithms at work in our lab. We have systems that can match isomorphic subgraphs and also match approximate graphs. Contact me if you need help. - Hasan

$\endgroup$
1
  • 3
    $\begingroup$ Would you mind adding some details? Not everyone has access to that paper. $\endgroup$ Dec 28, 2013 at 22:48

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.