[Insight-developers] Default boundary condition for WindowedSinc as constant?

[Nicholas Tustison]

I love that you can just run testing like that with only a couple lines.
That's really cool.  

Unfortunately, I don't know the answer to your question but Paul might.  
I'm cc'ing him on this and hopefully he'll see it and be able to answer.

Nick


On Dec 19, 2012, at 9:22 AM, Bradley Lowekamp <blowekamp at mail.nih.gov> wrote:

> Hello Nick,
> 
> Thanks for getting back to me on this.
> 
> I also ran the Sinc interpolators on a constant image, and I got a larger error than expected. The following Python code was run with the ZeroFlux boundary condition and the radius template parameter of 5:
> 
> # Create a image of all ones
> img = sitk.Image( 10, 10 , sitk.sitkFloat64 )
> img += 1
> 
> iterps = [sitk.sitkNearestNeighbor,
>          sitk.sitkLinear,
>          sitk.sitkBSpline,
>          sitk.sitkGaussian,
>          sitk.sitkHammingWindowedSinc,
>          sitk.sitkCosineWindowedSinc,
>          sitk.sitkWelchWindowedSinc,
>          sitk.sitkLanczosWindowedSinc,
>          sitk.sitkBlackmanWindowedSinc]
> 
> for i in iterps:
>    eimg= sitk.Expand( img, [10,10], i )
>    print "RMS:",(sum( (1-eimg)**2)/len(eimg))**.5, "Abs:", max(sitk.Abs(1-eimg))
> 
> RMS: 0.0 Abs: 0.0
> RMS: 0.0 Abs: 0.0
> RMS: 1.90178968104e-16 Abs: 5.55111512313e-16
> RMS: 0.0 Abs: 0.0
> RMS: 0.00519432546396 Abs: 0.007170554427
> RMS: 0.00111584107245 Abs: 0.00190357704047
> RMS: 0.000697067283848 Abs: 0.00118879124085
> RMS: 0.00143647177089 Abs: 0.00245097611656
> RMS: 0.000491351024756 Abs: 0.000833429218405
> 
> Skimming through the code it looks like the kernel is point sampled and not integrated over the pixel. I wonder if that is the issue.
> 
> Brad
> 
> On Dec 18, 2012, at 3:03 PM, Nicholas Tustison <ntustison at gmail.com> wrote:
> 
>> Hi Brad,
>> 
>> Yeah, we just use the default.  We've probably never noticed it since,
>> as you say, we typically are interpolating a blob in the middle of a black
>> background.
>> 
>> I think Paul Yushkevich wrote those windowed sinc interpolators.  You 
>> might want to ask him why they're the default.
>> 
>> Nick
>> 
>> 
>> 
>> On Dec 18, 2012, at 1:09 PM, Bradley Lowekamp <blowekamp at mail.nih.gov> wrote:
>> 
>>> Hello,
>>> 
>>> As I am finally integrating the different interpolators into SimpleITK. I am giving them a close look over.
>>> 
>>> The set of WindowSincInterpolateImageFunctions takes a Boundary condition template parameter. This defaults to ConstantBoundaryCondition. That is by default the pixels are zero outside the image, and they are not zero flux. This results in quite a bit of ringing and fading around my test images. It seems just wrong.
>>> 
>>> I can easily specify this parameter as the ZeroFluxNeumannBoundaryCondition (I don't think we have a mirror/reflective boundary, which is another possibility), and things look quite good and as I expect the output to be. I was curious as to what others were doing so I perused BRAINS and ANTS, grepping for the sinc interpolator. And to my surprise they are using the default!
>>> 
>>> Is there a reason that this default is preferred? Or is it that I am not processing a single blob in the center of a black image (aka a brain)?
>>> 
>>> Also in terms of consistency across the interpolators, this is the only one which takes a boundary condition template parameters. The other interpolators appear to behave sensibly, and exhibit a zero-flux type boundary condition. I think the default for this may need to be changed.
>>> 
>>> 
>>> I have this little example I have been working on in SimpleITK with the famed cthead1.png data input. Here is a code snippet:
>>> 
>>> 
>>> image = image[(size[0]//2-25):(size[0]//2+25),(size[1]//2-25):(size[1]//2+25)]
>>> 
>>> 
>>> iterps = [sitk.sitkNearestNeighbor,
>>>        sitk.sitkLinear,
>>>        sitk.sitkBSpline,
>>>        sitk.sitkGaussian,
>>>        sitk.sitkHammingWindowedSinc,
>>>        sitk.sitkCosineWindowedSinc,
>>>        sitk.sitkWelchWindowedSinc,
>>>        sitk.sitkLanczosWindowedSinc,
>>>        sitk.sitkBlackmanWindowedSinc]
>>> 
>>> eFactor=5
>>> 
>>> image_list = []
>>> 
>>> for i in iterps:
>>>  image_list.append( sitk.Expand( image, [eFactor]*3, i ))
>>> 
>>> tiles = sitk.Tile( image_list, [3,0] )
>>> 
>>> And the following is the output with the different boundary conditions:
>>> 
>>> http://erie.nlm.nih.gov/~blowek1/images/expand_interp_cbc.png
>>> http://erie.nlm.nih.gov/~blowek1/images/expand_interp_zfbc.png
>>> 
>>> Thanks for you feedback,
>>> Brad
>> 
>