[Mrtrix-discussion] SH coefficients ordering

[Donald Tournier]

Hi Ting,

I'm afraid the manual is wrong on this front. My apologies, I'll
update it for the next release. The ordering of the SH coefficients is
actually:

[index]    [l,m]     basis function
[0]           [0,0]    Y(0,0)

[1]           [2,-2]   Im {Y(2,2)}
[2]           [2,-1]   Im {Y(2,1)}
[3]           [2,0]    Y(2,0)
[4]           [2,1]    Re {Y(2,1)}
[5]           [2,2]    Re {Y(2,2)}

[6]           [4,-4]   Im {Y(4,4)}
[7]           [4,-3]   Im {Y(4,3)}
...

The indexing in MRtrix is done using the function (src/dwi/SH.h, line 36):
inline int index (int l, int m) { return (l*(l+1)/2 + m); }

and the best place to see how the basis functions are computed is in
the function:
void init_transform (Math::Matrix& SHT, const Math::Matrix& dirs, int lmax);
in src/dwi/SH.cpp, line 237

This is the ordering that's been used in MRtrix since the first
release. I'm not familiar with Camino, so I can't really answer your
second question. You might want to ask the Camino team about that, or
have a look through their documentation.

Hope that helps,

Donald.


On Thu, Sep 24, 2009 at 7:54 PM, Ting-Shuo Yo <tsyo at cbs.mpg.de> wrote:
> Dear mrtrix-users,
>
> I have two questions concerning the ordering of SH coefficients output from "csdeconv".
>
> I read from the on-line manual of csdeconv(http://www.brain.org.au/software/mrtrix/commands/csdeconv.html), that the SH ordering of this command is: Y(0,0), Y(2,0), Re-Y(2,1), Im-Y(2,1), Re-Y(2,2), Im-Y(2,2),....
>
> Q:
> 1. Is this ordering also used in earlier version (e.g., 0.2.5) ?
> 2. Does that mean I can directly use the output for Camino?
>
> Thanks in advance,
>
>
> Ting
>
>
> =============================================================
> Ting-Shuo Yo
> Max Planck Institute for Human Cognitive and Brain Sciences
> Stephanstr. 1a; 04103 Leipzig, Germany
> Fax: +49 (0)341 9940 2624    Tel: +49 (0)341 9940 2625
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--
Jacques-Donald Tournier (PhD)
Brain Research Institute, Melbourne, Australia
Tel: +61 (0)3 9496 4078