# Radius of Spherical ROI vs Cluster Size

Hi AFNI experts,

I'm wondering if someone could clarify the relation between spherical ROI radius and size of the cluster created when using 3dundump to create an spherical ROI. The voxel size for the scans is 3.5mm.

For example, the command I used was:

echo "10 12 -11" | 3dUndump -orient LPI -srad 6 -master AppvsRest_Dec_MPTn20+tlrc -prefix IB_RVS_ROI7mm+tlrc -xyz -

According to the cluster report on the mask I created, the size of the ROI is 19 vox. I would have thought that the ROI created would be larger than 19 voxels based on a radius of 6mm. Perhaps my issue lies with a misunderstanding of the units?

Thanks so much,
Carly

That radius is from voxel center to voxel center, so the radius distance will be the voxel size dimension only for voxels directly facing the center coordinate only for the facing voxels. Two voxel distance for the 3.5mm voxels will be 7mm away on the next facing voxel. You can use the pythagorean theorem to calculate the distance for voxels that share an edge (2D) or a corner (3D). For voxels that share an diagonally, those will have distance away from the center voxel of '3.5sqrt(2)'=4.95mm. The corner voxel will be '3.5sqrt(3)'=6.06 mm. So, if you want to catch those corner voxels, you will have to increase radius just a bit, say 6.07mm, and the neighborhood would be 27 voxels.

Hi, Carly-

Sure, I just did the same thing on my computer, and I get the same result.

It relates to what is discussed here:
https://afni.nimh.nih.gov/pub/dist/doc/htmldoc/FATCAT/MakingROIs.html#getting-to-know-your-neighbors

The thing is that 6mm is not a very large multiple of the voxel size. The ratio of radius-to-voxdim is 1.71 here: that just gets you a "face+edge" neighborhood of voxels around a centroid. If you increase the radius to 6.5 (or even 6.3), you will get a 27 voxel neighborhood.

Picture making a sphere of radius R, starting from the centroid (middle) of one voxel. For any neighboring voxel to be claimed by that sphere, its own centroid must fall within that radius. In any cardinal direction in the grid, one steps by voxel dims: so the facewise neighbor centroids are 3.5mm away, then along that direction the next closest is 7mm ----already outside the capture radius here.

-pt

That helps a lot! Thanks so much.