Hi Peter,<div><br>As René mentioned, the SH basis in MRtrix is not orthonormal - something that I hope will be fixed in a future major release. That said, I'm not sure this is the problem you're having, it wouldn't cause a pure rotation. </div>
<div><br></div><div>I'm struggling to understand the figure you sent through. The ODF doesn't look like it was displayed using MRtrix - what software was used for that, and what SH basis did it assume? What does the ODF look like when you display it using MRtrix's disp_profile command? Also, which directions are the peaks actually pointing along? The effect of the non-orthonormality of the basis will be different for peaks aligned along z than for peaks in the x-y plane, causing a differential scaling in this case. Also, you said the directions estimated by find_SH_peaks are correct, but they clearly don't match the ODF lobes as displayed. If so, and the ODF was not displayed using MRtrix, then I would suspect that whatever routine you use for display is at fault. Using disp_profile would at least verify that MRtrix is consistent with itself (i.e. the ODF lobes it displays should point along the directions estimated by find_SH_peaks). </div>
<div><br></div><div>Finally, If you're going to change the code in MRtrix, you'll need to know that there are a number of functions that compute SH functions, each coded up slightly differently (for performance reasons) - that said, they are all in the same file, so it's not difficult to modify them all. </div>
<div><br></div><div>Hope that helps,</div><div><br></div><div>Donald.</div><div><br></div><div><br><div class="gmail_quote">On 4 January 2013 01:22, Peter Neher <span dir="ltr"><<a href="mailto:p.neher@dkfz-heidelberg.de" target="_blank">p.neher@dkfz-heidelberg.de</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div bgcolor="#FFFFFF" text="#000000">
Hi René,<br>
<br>
thank you for your reply! Unfortunately that did not fix my problem.
I attached an image of the ODF I get with my method (negative Lobes
are dark blue). The red lines indicate the peaks extracted from the
SH coefficient file using "find_SH_peaks". These peaks are correct
but the ODF is somehow rotated. The ODF should actually represent a
simple 90° crossing of two fibers corresponding to the two peaks.<br>
<br>
Here a code snippet of my SH basis calculation. Maybe someone can
directly identify the issue:<br>
<br>
<small>j=0;<br>
for (int l=0; l<=ShOrder; l=l+2)<br>
for (m=-l; m<=l; m++)<br>
{<br>
// evaluation of legendre polynome<br>
float mag =
sqrt((double)(2*l+1)/(4.0*M_PI)*factorial<double>(l-abs(m))/factorial<double>(l+abs(m)))
* legendre_p<double>(l,abs(m),cos(sphCoords(0)));<br>
<br>
if (m<0)<br>
m_ShBasis(j) = sqrt(2.0)*mag*cos(-m*sphCoords(1));<br>
else if (m==0)<br>
m_ShBasis(j) = mag;<br>
else<br>
m_ShBasis(j) = pow(-1.0,
m)*sqrt(2.0)*mag*sin(m*sphCoords(1));<br>
<br>
j++;<br>
}</small><br>
<br>
I also tried it without the sqrt(2.0) and pow(-1.0, m) terms, but
that does not change anything. <br>
<br>
Best,<br>
Peter<br>
<br>
<div>On 01/03/2013 01:01 PM, René Besseling
wrote:<br>
</div>
<blockquote type="cite">
<div>Hi Peter,</div>
<div> </div>
<div>I ran into this before; it has to do with the MRtrix SH basis
being orthogonal but not orthonormal, see the following quote
from an e-mail from Donald.</div>
<div> </div>
<div>Best regards and happy new year to you too,</div>
<div><br>
René</div>
<div><br>
Quote Donald:</div>
<div>
<div>"To answer your question: the matlab code does use an
orthonormal basis, but MRtrix unfortunately does not. Main
reason is that I didn't bother checking that the basis was
orthonormal in the MRtrix code until relatively recently, and
it's now too late to change it without making all current data
sets ambiguous (i.e. how do you know whether a data set uses
the orthonormal basis or not?). I have since changed the
matlab code though, which is why there is a difference.</div>
<div><br>
</div>
<div>It's pretty easy to convert between them: the m=0 terms are
not affected, while the m!=0 terms are all scaled by a factor
of <span>sqrt</span>(<span>2</span>) in
MRtrix compared with Matlab. Easy to fix, but very annoying I
have to admit."</div>
<div><br>
<br>
</div>
</div><div><div class="h5">
<div class="gmail_quote">On Thu, Jan 3, 2013 at 12:54 PM, Peter
Neher <span dir="ltr"><<a href="mailto:p.neher@dkfz-heidelberg.de" target="_blank">p.neher@dkfz-heidelberg.de</a>></span>
wrote:<br>
<blockquote style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;border-left-style:solid" class="gmail_quote">Hi everyone and happy new year!<br>
<br>
I am trying to import the SH coefficient file (output of
csdeconv) into my own program but the ODFs are not displayed
correctly. The same method worked fine for the FSL coefficient
files so I guess you are calculating the SH basis in a
different way (the file format seems to be the same as the FSL
file format). MRview renders the ODFs correctly, so I wanted
to compare may code to the MRview code. Can you tell me the
location in the source code where I can find your calculation
and evaluation of the SH basis?<br>
<br>
Best,<br>
Peter<br>
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(DKFZ, Deutsches Krebsforschungszentrum in der Helmholtz-Gemeinschaft, Stiftung des öffentlichen Rechts)
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