[Mrtrix-discussion] curvature

[Donald Tournier]

Hi Michael,

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):

angle = 2 * asin (S / (2*R))

where:
  S = step-size
  R = radius of curvature

Hope that helps.
Cheers,

Donald.


On 6 June 2011 19:26, Thijs Dhollander <thijs.dhollander at uzleuven.be> wrote:

> 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:
>
> http://submissions.miracd.com/ismrm2011/proceedings/files/2019.pdf
>
> Kind regards,
> Thijs
>
> -----Original Message-----
> From: mrtrix-discussion-bounces at public.nitrc.org [mailto:
> mrtrix-discussion-bounces at public.nitrc.org] On Behalf Of Thijs Dhollander
> Sent: maandag 6 juni 2011 11:01
> To: mrtrix-discussion at public.nitrc.org
> Subject: RE: [Mrtrix-discussion] curvature
>
> Hi Michael,
>
> 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
> http://en.wikipedia.org/wiki/Curvature for some figures)
>
> 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.
> 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.
>
> I hope this explanation is somewhat clear. :-)
>
> Kind regards,
> Thijs
>
>
> Thijs Dhollander
> PhD Student
>
> 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
>
>
> -----Original Message-----
> From: mrtrix-discussion-bounces at public.nitrc.org [mailto:
> mrtrix-discussion-bounces at public.nitrc.org] On Behalf Of Michael Zeineh
> Sent: maandag 6 juni 2011 5:18
> To: mrtrix-discussion at public.nitrc.org
> Subject: [Mrtrix-discussion] curvature
>
> Question re the curvature parameter in streamtrack.
>
> 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.
>
> How does "curvature radius" in mm translate in the above conventional
> angular terms as used in streamtrack?
>
> Thank you,
> Michael Zeineh
>
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-- 
Jacques-Donald Tournier (PhD)
Brain Research Institute, Melbourne, Australia
Tel: +61 (0)3 9035 7033
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