[Mrtrix-discussion] curvature

[Thijs Dhollander]

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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