[Mrtrix-discussion] Tensors in mrview

[Thijs Dhollander]

Hello everyone,

The analytic expression to convert forth and back between SH coefficients and tensor parameters has been described in this paper from Descoteaux et al. (2006):

http://onlinelibrary.wiley.com/doi/10.1002/mrm.20948/full

...more specifically, matrix M in equation 17, of which the solution for the rank-2 tensor and SH basis up to order 2 is shown in figure 3.  Be careful however, as this assumes the orthornomal SH basis that Maxime Descoteaux defined in that paper in equation 11 (and typically used in most of his following works).  The SH basis used in MRtrix is slightly different; a description of it can be found at e.g.

http://www.brain.org.au/software/mrtrix/commands/dwi2SH.html

The differences are the omission of the conventional (-1)^m factor, as well as an additional factor sqrt(2) for the Y(l,m) coefficients where m is not 0.

Cheers,
Thijs

Thijs Dhollander
PhD Student

thijs.dhollander at uz.kuleuven.ac.be<mailto:thijs.dhollander at uz.kuleuven.ac.be>
tel. +32 16 34 90 37
gsm. +32 475 36 44 27

Medical Image Computing (K.U.Leuven, ESAT/PSI, MIC)
Medical Imaging Research Center | UZ Gasthuisberg | Herestraat 49 - bus 7003 | B-3000 Leuven | http://www.medicalimagingcenter.be

From: mrtrix-discussion-bounces at public.nitrc.org [mailto:mrtrix-discussion-bounces at public.nitrc.org] On Behalf Of René Besseling
Sent: Saturday, October 27, 2012 11:31
To: Ariel Rokem
Cc: Arnaud Boré; mrtrix-discussion at public.nitrc.org
Subject: Re: [Mrtrix-discussion] Tensors in mrview

There is this analytical expression to express g'Dg in spherical harmonics, but it'quite a while back that I looked into that. I'll check in on monday on my pc at work.

René
On Sat, Oct 27, 2012 at 1:47 AM, Ariel Rokem <arokem at gmail.com<mailto:arokem at gmail.com>> wrote:
Hi Rene,

I would actually like to see that. Is there an analytic expression for that, or do you perform some kind of approximation? Could you put the code somewhere (e.g. gist.github.com<http://gist.github.com>)?

Thanks,

Ariel

On Fri, Oct 26, 2012 at 3:41 PM, René Besseling <r.m.h.besseling at gmail.com<mailto:r.m.h.besseling at gmail.com>> wrote:
Jep, you can express their peanut-shaped representation (so not the ellipsoid) in spherical harmonics. If you're interested, I've got a Matlab script that takes the dt.nii from dwi2tensor as an input at outputs the SH representation.

René
On Fri, Oct 26, 2012 at 8:10 PM, Arnaud Boré <arnaud.bore at gmail.com<mailto:arnaud.bore at gmail.com>> wrote:
Hello MRtrix users,

Just want to know if there is a way to see tensors in mrview.

Thanks
Arnaud

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