[Insight-users] What is the *correct* way to downsample an image with ITK?

[Jonathan Orban]

Hi Joel,

You are right about the fact that in order to do proper signal 
downsampling, you need to start by filtering the signal with a low-pass 
filter. This is required to respect the Nyquist-Shannon theorem ( 
<http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem> ).

In the fields where the images are sampled representations of a real 
signal (such as medical imaging), it is common to use a scale-space 
representation of the signal, that is, a framework to "handle image 
structures at different scales, by representing an image as a 
one-parameter family of smoothed images, parametrized by the size of the 
smoothing kernel used for suppressing fine-scale 
structures".(<http://en.wikipedia.org/wiki/Scale_space>)

There are different families of kernels that allow you to do such 
operation. However, the Gaussian filter is the canonical way to generate 
a linear scale-space. 
(<http://en.wikipedia.org/wiki/Scale_space#Why_a_Gaussian_filter.3F>)

There are plenty of scientific articles and books referenced on these 
wikipedia pages where you will find all the information that you need.

HTH,

Jonathan

Joel Schaerer wrote:
> Hi Dan,
>
> Thanks for your answer. I've already looked at that paper, but it only
> considers the choice of the interpolation function. My understanding is that
> for image downsampling, regardless of the interpolation function you use,
> you have to apply a low-pass filter to the image prior to resampling in
> order to avoid aliasing effects. My question is about this low-pass
> filtering step, not the interpolation function.
>
>
>
> Dan Mueller-2 wrote:
>   
>> Hi Joel,
>>
>> You may be interested in the following paper:
>>
>> http://www.imagescience.org/meijering/publications/download/miccai1999.pdf
>> @inproceedings{Meijering1999a,
>>    Author = {E. Meijering and W. Niessen and J. Pluim and M. Viergever},
>>    Title = {Quantitative Comparison of Sinc-Approximating Kernels for
>> Medical Image Interpolation},
>>    Booktitle = {Proceedings of Medical Image Computing and
>> Computer-Assisted Intervention (MICCAI)},
>>    Page = {210--217},
>>    Publisher = {Springer},
>>    Volume = {1679},
>>    Year = {1999}
>> }
>>
>>
>>
>>     
>
>   


-- 
Jonathan Orban
_________________________________________________________

Researcher, PhD Student (FRIA) - Medical Image Processing

Communications and Remote Sensing Laboratory (TELE),
Université catholique de Louvain (UCL),
Batiment Stévin
Place du Levant, 2
B-1348 Louvain-la-Neuve, Belgium

Tel: +32(0)10/47.80.74 - Fax: +32(0)10/47.20.89 
email: jonathan.orban at uclouvain.be