[Elastix] Coordinates of control points in B-spline transform

Ramón Casero Cañas rcasero at gmail.com
Thu Apr 16 22:38:47 CEST 2015


Thanks, Coert and Stefan, very useful.

(On an unrelated note, Coert, citing your 2011 MIA paper in something I'm
writing, by coincidence :) )

Best regards,

Ramon.

On 15 April 2015 at 22:09, S. Klein <s.klein at erasmusmc.nl> wrote:

>  Hi Ramon, Coert, the ordering of the parameters is indeed as you mention.
> Best,
> Stefan
>
>
> On 15-4-2015 22:15, Coert Metz wrote:
>
> Dear Ramón,
>
>  The code that computes the grid origin and spacing is (if I am not
> mistaking) in src/Common/Transforms/itkGridScheduleComputer.hxx of the
> elastix sources. Also the TransformParameters.*.txt file should list the
> GridSpacing, GridSize, GridIndex and GridOrigin from which you can deduce
> this information. All points are equidistant for sure. If I remember
> correctly the ordering of the parameters is indeed as you mention.
>
>  Regards,
> Coert Metz
>
> On Wed, Apr 15, 2015 at 7:56 PM, Ramón Casero Cañas <rcasero at gmail.com>
> wrote:
>
>> Dear all,
>>
>>  I have a couple of questions about B-splines in elastix:
>>
>>  1) What are the coordinates of the control points in a B-spline
>> transform?
>>
>>  After registering an image to itself, the t.TransformParameters are all
>> zero, as expected for no deformation.
>>
>>  But how's the grid determined, e.g. for a cubic spline?
>>
>>  Let's say e.g. that we have a 1D grid with 5 control points, plus 1
>> extra point before the grid, plus 2 extra points after the grid, in each
>> dimension.
>>
>>  Are the coordinates of the 5 control points determined by placing one
>> at the centre of the first pixel, and another at the centre of the last
>> pixel, and then the other 3 equidistant between those?
>>
>>  2) Are then the extra ones outside the grid, and equidistant too?
>>
>>  3) Is the convention for the TransformParameters [x1 x2 x3...xN y1 y2
>> ... yN]?
>>
>>
>>  Best regards,
>>
>>  Ramon.
>>
>>  --
>>  Dr. Ramón Casero Cañas
>>
>> Institute of Biomedical Engineering
>> Department of Engineering Science, University of Oxford
>> Old Road Campus Research Building, Headington
>> Oxford
>> OX3 7DQ
>> UK
>>
>> tlf         +44 (0) 1865 617716
>> twitter   @Ramon_Casero
>> web      http://www.cs.ox.ac.uk/people/Ramon.CaseroCanas/
>>
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>>
>
>
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-- 
Dr. Ramón Casero Cañas

Institute of Biomedical Engineering
Department of Engineering Science, University of Oxford
Old Road Campus Research Building, Headington
Oxford
OX3 7DQ
UK

tlf         +44 (0) 1865 617716
twitter   @Ramon_Casero
web      http://www.cs.ox.ac.uk/people/Ramon.CaseroCanas/
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