[MINC-users] Resampling a minc volume while conserving intensity

[Vladimir S. FONOV]

you need a mass preserving transformation, where the total sum over all voxels of interest stays constant. I would convert counts in the input volume to the density (i.e divide counts by the volume of each voxel). Then resample to the target volume, and finally, multiply by the jacobin determinant of the inverse transformation calculated in the target space (if your transformation is linear, it is equivalent of deviding by the jacobian of the transformation matrix from source space to target space). And finally - multiply densities by the volume of voxel in the target space to convert from densities to counts. 


> On Sep 29, 2018, at 12:20, Nick Wang <nick.wang at sickkids.ca> wrote:
> 
> Hello everyone,
> 
> 
> In a registration pipeline, I have a minc volume where each voxel's intensity represents the number of cells in that voxel in physical space. I would like to resample this minc volume nonlinearly to align with an atlas. Mincresample's trilinear resampling does not conserve these counts (intensities) properly. Imagine having a adjacent voxels of intensities 10, 10 and 1 being transformed really close to each other, then I may have a result like 5.5, 5.5, and 5.5
> 
> 
> As a rough workaround, I tried multiplying the minc volume by the determinant of the inverse of the transform (as one does with triple integrals), but I believe the discrete nature of minc volumes causes error as well. Imagine having a voxel of intensity 10 being shrunk by a factor of 4, but stays exactly in place. I believe this method would cause the transformed voxel to have an intensity of 40 in the outcome. Even if my reasoning here is wrong, this seems like much of a bandaid solution.
> 
> 
> Does anyone have any ideas or have any experience with this? Essentially, I am looking for a resampler that conserves the "local" sums of intensity - local enough such that if I take the sum of the intensities of some small region of voxels in the original minc volume, I should get the same sum as the intensities of the corersponding voxels in the transformed volume.
> 
> 
> Thanks,
> 
> Nick
> 
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Best regards, Vladimir S. FONOV ~ v.s.fonov <at> ilmarin.info