[Mrtrix-discussion] Tracks2prob colour TDI for deformed tracks

[Robert Smith]

Daan

Hopefully I get these correct (it's been a while since I've worked with the
0.2 code):

1. The Hermite interpolation ("Resampler" class) generates samples that are
equidistant on the Hermite spline (i.e. in terms of the interpolation
coefficient 'mu' for interpolating a point between two samples). So
depending on the shape of the spline (and the spacing of the input
streamline points), they may not be perfectly equidistant in Euclidean
space, but it's not far from it. A non-linear warp field would probably
have a larger influence on this non-equidistant-ness than the interpolation
step.

2. Each tangent of the streamline is normalised (tracks2prob.cpp, lines 328
and 335). So each streamline point within a voxel (post Hermite
interpolation) contributes equally to the mean tangent of the streamline
within that voxel.

In general I wouldn't be too concerned about the preciseness of a DEC TDI
map; the colour hue is intended for visualisation and not for quantitative
purposes. If however you have an application that demands accurate
determination of these tangents, the next major MRtrix release will include
the code for my improved streamline mapping method (SIFT paper,
appendix 3<http://www.sciencedirect.com.ezp.lib.unimelb.edu.au/science/article/pii/S1053811912011615#appd003>),
which can be used in the generation of DEC TDIs (or used for your own
purposes). Because it maps the streamline to the voxel edges instead of
just 'up-sampling' it, the tangent and the length of the streamline through
each voxel are calculated more accurately.

Any other questions or concerns let me know
Rob


--

Robert Smith
PhD Candidate

The Florey Institute of Neuroscience and Mental Health
Melbourne Brain Centre - Austin Campus
245 Burgundy Street
Heidelberg Vic 3084
Ph: +61 3 9035 7128
Fax: +61 3 9035 7301
www.florey.edu.au


On Fri, Jan 18, 2013 at 12:25 AM, Daan Christiaens <
Daan.Christiaens at esat.kuleuven.be> wrote:

>  Dear all,
>
>  I am trying to calculate the colour TDI map of a full-brain track set
> that was generated in subject space and warped (non-rigidly) to atlas space
> using the 'normalise_tracks' command. In doing so, however, the distance
> between successive samples on each track can change. This got me thinking
> about the calculation of the colour TDI: as each track contributes to the
> colour in each voxel it crosses by the average of the tangent vectors in
> all samples, an unequal distance between successive samples could have an
> effect on the colour, especially if the distance between samples also
> affects the size of the tangent vectors.
>
>  The 'tracks2prob' command allows to specify a resampling factor, which
> might solve this issue if it would ensure equidistant samples. Thijs and I
> have been looking at the code to see if this is indeed the case, but we
> can't quite figure it out. So basically, I have 2 questions:
>
>    1. Does Hermite interpolation in the tracks2prob command generate
>    samples at equal distance, or will it only add (let's say 5) samples
>    between every pair of original samples?
>    2. Does the distance between successive samples influence the size of
>    the tangent vectors that contribute to the RGB colour? In other words, are
>    the tangent vectors in all samples normalised before averaging, or will
>    samples that are further apart have a larger contribution to the colour TDI?
>
>
>  Many thanks and kind regards,
>
>  Daan
>
>
>   *ir. Daan Christiaens*
> Ph.D. Researcher
>
> * <daan.christiaens at uzleuven.be>daan.christiaens at esat.kuleuven.be*
> tel +32 16 34 90 42****
> fax +32 16 34 90 01****
>
>
> *Medical Image Computing – ESAT/PSI – Department of Electrical Engineering
> *
>
>
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