Hi Jan,

the MorphologicalGraph algorithm was developed and implemented by me four years ago. I am not aware of any preexisting or established algorithms to refer to, nor a publication with respect to this matter.

You can find an unambiguous description of the MorphologicalGraph-result on the reference page under "Detailed and Options".

The processing steps are fairly straight forward:

1. apply Binarize[Thinning[img, Method -> "Morphological", Padding -> 0]] upfront to obtain a skeleton,
2. find the vertices given by branch and end-points (use MorphologicalTransform[skeleton, "SkeletonEndPoints", Padding -> 0] and MorphologicalTransform[skeleton, "SkeletonBranchPoints", Padding -> 0]),
3. remove vertices and find link-components,
4. identify which vertices are connected by which links,
5. remove links that loop back to the same vertex,
6. remove redundant links,
7. assemble everything in an undirected Graph object.

For details, see the top-level code via: Unprotect[MorphologicalGraph] ClearAttributes[MorphologicalGraph, ReadProtected] ?? MorphologicalGraph ?? ImageMorphologicalOperationsDumpiMorphologicalGraph ?? ImageMorphologicalOperationsDumpoMorphologicalGraph

Hope that helps!

Please cite Mathematica in your article: Wolfram Research, Inc., Mathematica, Version 8.0, Champaign, IL (2010).

Kind Regards, Markus