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I am looking for a method or algorithm to produce a value that describes how different two meshes are geometrically but that have different topologies.

An example would be some CAD data that has had an FE mesh applied and the part after it has been manufactured and then scanned into a 3d triangulated mesh. The manufactured part will be slightly different geometrically from the CAD part, but in addition, the meshes that have been applied are totally different.

What is a good method to produce a measure of how similar or dissimilar they are geometrically.

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  • $\begingroup$ I don't know if I correctly understand what you want. In essence, you want to compare the boundaries of two meshes? Since the interior are geometrically the same. $\endgroup$ – nicoguaro Nov 4 '14 at 16:06
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The Hausdorff distance is a measure of how different two arbitrary sets in a metric space are, independent of topology. The open-source software MeshLab lets you compute the Hausdorff distance between two meshes.

Beware that the Hausdorff distance does not account for translation or rotation, so in case the meshes are misaligned you will have to register them first. MeshLab can help you do that too.

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I'm not sure it really helps, but you may have a look to temperature distribution on both mesh and compute a similarity measure between the two distributions. This is done in the following paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.385.5918

Cheers !

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  • $\begingroup$ This approach looks very interesting, but (in my very quick flick through) the paper seems to only test perturbing the locations of the mesh vertices, not changes in mesh topology, and its not clear to me that the method would hold should the topology change. $\endgroup$ – Michael Anderson Oct 8 '14 at 4:38
  • $\begingroup$ Also since the technique is designed to produces results that give the same value on semi-rigid model changes it seems inappropriate for the OPs need. $\endgroup$ – Michael Anderson Oct 8 '14 at 4:40

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