[Insight-users] bug in itkBSplineInterpolationWeightFunction?

[Stefan Klein]

Hi all,

Three weeks ago i posted the following mail (see also below this email):

http://public.kitware.com/pipermail/insight-users/2006-October/019744.html

concerning a possible bug in the itkBSplineInterpolationWeightFunction. Has 
anybody looked at this maybe? Should I add it as a bug entry in the bug 
tracker, or is it not a bug maybe?

See also a followup mail that i sent:
http://public.kitware.com/pipermail/insight-users/2006-October/019747.html

Kind regards!
Stefan.




>Hi,
>
>I think i found a bug in the implementation of the 
>BSplineInterpolationWeightFunction.
>
>In the Evaluate function, at lines 146-151, the startIndex of the support 
>region is computed, given a continuous input index (denoted by 'index'):
>
>   // Find the starting index of the support region
>   for ( j = 0; j < SpaceDimension; j++ )
>     {
>     startIndex[j] = static_cast<typename IndexType::IndexValueType>(
>       BSplineFloor( index[j] - static_cast<double>( SplineOrder / 2 ) ) );
>     }
>
>
>If I understand well, for a zero order bspline, this formula should result 
>in a 'round' operation. This is not the case with the formula above:
>
>suppose the continuous input index = 0.9 and the SplineOrder = 0.
>then:
>
>startindex = floor( 0.9 - 0/2 ) = floor (0.9) = 0.
>
>Consequently, in line 161, where the bsplinekernel weight is evaluated, 
>the result is zero.
>BsplineZeroOrder( inputindex - startindex ) = BSplineZeroOrder( 0.9 ) = 0.0.
>Which must be wrong, since for a zeroth order bspline the weight value 
>should be nonzero everywhere in its support region.
>
>For splineorder=1 the formula works. For splineorder=2 it goes wrong again 
>and for splineorder=3 it works. So, it's wrong for even spline orders.
>
>I suggest changing it to:
>
>      startIndex = floor( inputIndex + bsplineoffset )
>
>  where
>
>     bsplineOffset =  0.5 - static_cast<double>(SplineOrder) / 2.0 ;
>
>which results in bsplineOffset = 1/2, 0, -1/2, or -1 respectively for 
>order 0, 1, 2, and 3.
>
>In the case of zero order bspline this obviously gives the desired round 
>operation (floor(input+0.5)).
>In general: for odd spline orders it works the same as the current 
>formula, but for even orders the result is different.
>
>Please let me know if I made a mistake, or if it's really a bug.
>
>Kind regards,
>Stefan.

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