[MINC-users] mincblur with FWHM =?utf-8?Q?<=3D_?=voxel dims

[Alex Zijdenbos]

I've been wondering for some time what happens when you (minc)blur a volume with a FWHM that is about the same or less than the voxel dimension. Admittedly I am rather rusty on the intricate and practical details of scale space/FFT/convolution/etc, so this may well be showing my ignorance; but hopefully there are people on this list smarter than me who can enlighten me :)  

Empirically, when you reduce the FWHM to below the voxel dimension, the voxel value of the blurred image increases. Moreover, for an image with 1mm isotropic voxels, the FWHM at which the voxel values of the result are about equivalent to those in the source image seems to be around 1.3, give or take. See this image:  
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mni_icbm_00102_t1_blurs.png (http://cl.ly/2A1m3Y470P0M3S3J2Q0j)

which shows in the top row the original, 1mm isotropic, volume, followed by the result of running mincblur on it with decreasing FWHM from 1.5 to 0.5mm. I used spectral with a fixed range across all rows to bring out the signal difference.

So - is this expected? Surprising? Follows theory or bad behaviour of mincblur? After scribbling a few pages with normal distributions and looking through the mincblur code I still can't quite figure it out. Anybody can explain this to me?

Thanks,

-- Alex

PS In case you are wondering why one would want to do this, the answer is probably: you don't; but  one of the nice things about MINC is that as a user I don't need to care too much about pesky things like voxel dimensions, so let's say you have a script that blurs with a 2mm FWHM and you happen to pass that an image with 4mm voxels, you will end up with a more than 6-fold signal increase that you probably didn't expect (e.g., run a PET image through an MRI registration script). I could also imagine that in certain circumstances it might bite other blurring-dependent analyses (e.g., fMRI, VBM).