Hi ITK Community!

Sanity check here about Nyquist-Shannon sampling theorem and resampling images to be isotropic. I have read through the online example [1]. I have also read the sinc approximation paper [2].

**Setup** I have CT data that is captured at 0.5 x 0.5 x 2.0 mm resolution. I want my data in 1.0 x 1.0 x 1.0 mm resolution for quantification purposes (FEA, actually).

**Theory** Following classsic DSP theory, I would do the following.

I apply a low pass filter (say Gaussian) in the X and Y directions at a spatial frequency of 0.5 mm^-1 (Sampling frequency is 1 mm^-1 so Nyquist frequency is 0.5 mm^-1).

Then, I would drop samples in X and Y and zero order hold in Z.

Then, I would apply a low pass filter in Z at 0.5 mm^-1.

This all makes sense from a classic DSP approach. I avoid aliasing in X and Y with prefiltering and I get a reconstructed filter with postfiltering in Z.

**Interpolation Filter** The problem arrises with the concept of interpolation in the ITK Resample filter.

In the online example [1], X and Y are blurred with a Gaussian filter and a linear interpolator is used for resampling. Let’s say I use a Hamming Windowed Sinc interpolator. I map a point from the isotropic image to the fixed image, sample by convolving the Hamming Windowed Sinc, and store that value. This effectively causes blurring in my input image, similar to the effect of prefiltering.

**Question** If I use a proper interpolation filter (3rd order BSpline, windowed sinc) I do not have to prefilter my image. I will have minimal aliasing because I am effectively prefiltering my image in the interpolator. Is this correct?

[1] https://itk.org/Doxygen/html/Examples_2Filtering_2ResampleVolumesToBeIsotropic_8cxx-example.html

[2] https://www.researchgate.net/profile/WJ_Niessen/publication/221401597_Quantitative_Comparison_of_Sinc-Approximating_Kernels_for_Medical_Image_Interpolation/links/0deec525e649cb45a6000000/Quantitative-Comparison-of-Sinc-Approximating-Kernels-for-Medical-Image-Interpolation.pdf