Anisotropic Fast Marching

[donghaozhang]

I am a researcher who is doing research about tubular shape related segmentation and tracking and I applied multi-stencil fast marching in my previous project. I find one of your numerical tour is about anisotropic fast marching and I am currently studying your code. I am new to anisotropic fast marching. I have to say your code is amazing. Is that possible for you to post some related math behind anisotropic fast marching code(fm2dAniso.h)? Thank you so much for the amazing numerical tour anyway!

Kind regards,
donghao

[gpeyre]

You can find it for instance in our review paper, especially in Section 3.4 (it is described on a triangulation, but the same apply on a grid by considering 4 or 8 neighboring triangles around each point).

[donghaozhang]

Thank you so much!

[tvercaut]

Apologies for reviving an old thread but I am also interested in digging a bit more into anisotropic fast marching for cartesian grids (images). I tried looking at the code and the review paper listed above but got a bit confused. Would it be possible to share a bit more insight?

Section 3.4 of the review paper doesn't specifically talk about anisotropic fast marching. A quick bibliography search point to a few potential options, e.g.:

• https://doi.org/10.1137/120861667
• https://doi.org/10.1007/978-3-540-73273-0_57
• https://doi.org/10.1155/2008/320195
• http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-54344

It would thus be helpful to better understand what is implemented in the fastmarching_3_anisotropy notebook.
Indeed, looking at this fastmarching_3_anisotropy notebook, I see it calls fm2dAniso but that files doesn't provide much comments on the method being implemented.

I also saw the perform_front_propagation_anisotropic.cpp file but this refers to files that are missing from the repository: anisotropic-fm/AnisotropicTensorDistance.h and anisotropic-fm/AnisotropicTensorDistanceConfidence.h. I tried looking for these but only found this which may or may not be related:
https://github.com/gjacopo/imtools/blob/master/propagation/src/GCM/AnisotropicTensorDistanceConfidence.h