<div>Hi Michael,</div><div><br></div><div>Thijs is right on the money with his explanation. Just for reference, the actual expression relating step-size and radius of curvature to the angle between successive steps is (src/dwi/tractography/tracker/base.h, line 83):</div>
<div><br></div><div>angle = 2 * asin (S / (2*R))</div><div><br></div><div>where:</div><div> S = step-size</div><div> R = radius of curvature</div><div><br></div><div>Hope that helps.</div><div>Cheers,</div><div><br></div>
<div>Donald.</div><div><br></div><br><div class="gmail_quote">On 6 June 2011 19:26, Thijs Dhollander <span dir="ltr"><<a href="mailto:thijs.dhollander@uzleuven.be">thijs.dhollander@uzleuven.be</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">One extra warning though (just popped into my mind): this does of course not mean that the stepsize has no impact at all on the final result! Here goes a clear (and quite recent) example concerning the effect of the stepsize om probabilistic tractography:<br>
<br>
<a href="http://submissions.miracd.com/ismrm2011/proceedings/files/2019.pdf" target="_blank">http://submissions.miracd.com/ismrm2011/proceedings/files/2019.pdf</a><br>
<br>
Kind regards,<br>
<font color="#888888">Thijs<br>
</font><div class="im"><br>
-----Original Message-----<br>
From: <a href="mailto:mrtrix-discussion-bounces@public.nitrc.org">mrtrix-discussion-bounces@public.nitrc.org</a> [mailto:<a href="mailto:mrtrix-discussion-bounces@public.nitrc.org">mrtrix-discussion-bounces@public.nitrc.org</a>] On Behalf Of Thijs Dhollander<br>
Sent: maandag 6 juni 2011 11:01<br>
To: <a href="mailto:mrtrix-discussion@public.nitrc.org">mrtrix-discussion@public.nitrc.org</a><br>
</div><div><div></div><div class="h5">Subject: RE: [Mrtrix-discussion] curvature<br>
<br>
Hi Michael,<br>
<br>
Imposing a certain curvature radius threshold on the tracks means that they cannot bend in a sharper way than a circle (or a sphere) with that particular radius does. If the curvature radius threshold is smaller, tracks are allowed to bend sharper. (also see <a href="http://en.wikipedia.org/wiki/Curvature" target="_blank">http://en.wikipedia.org/wiki/Curvature</a> for some figures)<br>
<br>
My guess as to why MRtrix offers this option instead of an "angle threshold", is that the curvature radius has the advantage of defining the maximum "sharpness" of the tracks independently from the stepsize.<br>
For example, if you were to impose an angle threshold of 40 degrees, this number by itself does not define how sharp your tracks can globally bend: if your stepsize would be 1mm, the tracks could bend sharper as compared to a stepsize of 2mm. But, if you specify a certain curvature radius threshold, you can still play around freely with the stepsize without changing the maximum bending properties of your tracks.<br>
<br>
I hope this explanation is somewhat clear. :-)<br>
<br>
Kind regards,<br>
Thijs<br>
<br>
<br>
Thijs Dhollander<br>
PhD Student<br>
<br>
<a href="mailto:thijs.dhollander@uz.kuleuven.ac.be">thijs.dhollander@uz.kuleuven.ac.be</a><br>
tel. +32 16 34 90 37<br>
gsm. +32 475 36 44 27<br>
<br>
Medical Image Computing (K.U.Leuven, ESAT/PSI, MIC)<br>
Medical Imaging Research Center | UZ Gasthuisberg | Herestraat 49 - bus 7003 | B-3000 Leuven | <a href="http://www.medicalimagingcenter.be" target="_blank">http://www.medicalimagingcenter.be</a><br>
<br>
<br>
-----Original Message-----<br>
From: <a href="mailto:mrtrix-discussion-bounces@public.nitrc.org">mrtrix-discussion-bounces@public.nitrc.org</a> [mailto:<a href="mailto:mrtrix-discussion-bounces@public.nitrc.org">mrtrix-discussion-bounces@public.nitrc.org</a>] On Behalf Of Michael Zeineh<br>
Sent: maandag 6 juni 2011 5:18<br>
To: <a href="mailto:mrtrix-discussion@public.nitrc.org">mrtrix-discussion@public.nitrc.org</a><br>
Subject: [Mrtrix-discussion] curvature<br>
<br>
Question re the curvature parameter in streamtrack.<br>
<br>
I am familiar with curvature being a threshold such that a track won't make a turn of more than 40 degrees or whatever threshold is chosen.<br>
<br>
How does "curvature radius" in mm translate in the above conventional angular terms as used in streamtrack?<br>
<br>
Thank you,<br>
Michael Zeineh<br>
<br>
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</div></div></blockquote></div><br><br clear="all"><br>-- <br>Jacques-Donald Tournier (PhD)<br>Brain Research Institute, Melbourne, Australia<br>Tel: +61 (0)3 9035 7033<br>