implementation as a submodule in slam with proper unittest, doc and examples

[JulienLefevreMars]

• Examples are done: plot on the mesh of the local dominance bands in a very general setting (more than 7 bands)
• 3 unit-tests, one last missing

[annekerachni]

Examples & proper visualization:

• Mireia and I have planned to work this week on some visualization inputs to the current Spangy. We would like to define a "manual" and generalizable colormap to display the local dominant bands, global coefficients and compacted spectrum of the mean curvature with the same aspect.

  In this context:

  • Does it make sense "divide" the mean curvature signal into the two subsignals $meancurv<=0$ and $meancurv>0$ and then to compute separately raw coefficients and global compacted spectrum representing either folding pattern in sulci either folding pattern in gyri?
  • Details: If Laplace-Beltrami operator is linear and we use $meancurv = (meancurv<=0) + (meancurv>0)$, we can decompose the same way the whole signal or either part of the signal onto the whole brain eigenfunction basis, can't we? So, I have the feeling that coefficients could be computing separately for sulci and for gyri, but maybe not the global compacted spectrum. What do you think?

  If there is no interest to spend time on that, we can also let the coefficients and global compacted spectrum plot as it is.

[JulienLefevreMars]

Yes, the LBO is linear. The same for a spectral decomposition of the sum of two functions, but because of properties on euclidean space (Hilbert space in the continuous domain). So yes, it makes sense to divide the mean curvature like this. The only problem that I can see is that the two functions you obtain are vanishing by parts. So it can require more high frequency coefficients to model the discontinuity in the derivative between the regions with meancurvature=0 and the others. But it could be interesting to be tried :-)

[annekerachni]

Thank you Julien! So, maybe we can notify to use a high number of eigenpairs (N) to have a "good" approximation of each global spectrum of the subsignals (folding pattern in gyri and folding pattern in sulci)?

The idea was to get displays of that type (see below), coherent with the colormap used for to display the local dominant band.

[annekerachni]

In your paper, you also mentioned "normalized spectrum of curvature". Is it better to refer to raw spectrum or rather normalized one?