[Neuroimaging] [Dipy] discrepancies of SH coeffs with MRtrix

[Ariel Rokem]

Hi Eric,

Thank you for your message, and for taking the time to figure these things
out together.

On Wed, Oct 19, 2016 at 12:55 AM, Eric Moulton <eric.moulton.jr at gmail.com>
wrote:

> Hello Dipy contributors,
>
> I have been playing with Dipy recently in hopes that I can use it as the
> main tool to process my data. In particular, I have been interested in
> using MRtrix's mrregister which is linear/non-linear registration technique
> based on the SH coefficients (http://www.sciencedirect.com/
> science/article/pii/S1053811911001534#bb0285).
>
> The papers results have reported that the best registration is obtained
> with lmax = 4, so I have calculated the SH coefficient volumes with Dipy
> and MRtrix. In Dipy, I did this with peaks_from_model function and making
> sh_basis_type='mrtrix' and then using the shm_coeff attribute. In MRtrix, I
> used the dwi2fod function. I can develop on this more if you require more
> details. In short, both gave me 4D volumes with 15 volumes in the 4th
> dimension as expected for lmax = 4.
>
> The first thing I noticed when I compared the two outputs was that the
> Y(0,0) volume in Dipy was a single value brain volume where every voxel
> coefficient was equal to 0.2821 - which is literally the equation for
> Y(0,0) = 1/sqrt(4*pi) - whereas the Y(0,0) volume had different
> coefficients for each voxel. I contacted them about this, and they did a
> really good job explaining it to me (http://community.mrtrix.org/t
> /first-spherical-harmonic-coefficient-y-0-0-meaning/507/1). In short,
> they said that Dipy normalizes to the unit integral whereas MRtrix doesn't.
>

I'm sorry -- I might be misunderstanding what you -- but I am unable to
reproduce this. When I run this example:

http://nipy.org/dipy/examples_built/reconst_csd.html

setting the `sh_order` keyword argument of `ConstrainedSphericalDeconvModel`
to 4 (line 170), and then plotting the first slice in the `sh_coeff`
attribute of the fit object, corresponding to Y(0, 0), I get a spatially
varying function, as you would expect.

Maybe you could tell me what exactly you are doing? Are you by any chance
looking at the basis set itself (`csd_model.B_dwi[..., 0]`)? That should be
a constant for Y(0,0) -- it's a sphere, after all. And indeed, it's all
equal to 1/sqrt(4pi).

Cheers,

Ariel

As I said, my main goal is to use use mrregister and in particular with the
> IIT HARDI template (https://www.nitrc.org/frs/?group_id=432) which has
> the same MRtrix SH coefficient system (i.e. Y(0,0) is different for every
> voxel). But to do that with Dipy, I imagine that I would need to have
> similar SH coeff outputs for my data. I have tried playing with the Dipy
> code to obtain similar results as with MRtrix (taking out the normalization
> term in spherical_harmonics(m,n,theta,phi) in dipy/reconst/shm.py, etc.)
> but I still keep getting a single valued brain for the Y(0,0) term that
> equals 1/sqrt(4*pi).
>
> I was wondering if someone know where this difference in behavior is
> coming from and where I could look to try to get MRtrix-type outputs for
> the SH coeffs.
>
> Thank you for your time,
> Eric
>
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