3D Mean Filter: How is it computed?


Could anyone expalin me how the 3D mean filter works in Fiji (ImageJ)?

In the ImageJ documentation the only description is: “3D filtering using ellipsoidal neighbourhood” I dont really get how it calculates the voxels in the kernel. (https://imagejdocu.tudor.lu/doku.php?id=plugin:filter:3d_filters:start)

How many voxels are taken in the kernel? And how are they calculated?

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Hello Pedro -

I assume that you are talking about the filter that is run from:
Process > Filters > Mean 3D....

Let xo, yo, and zo be the integer voxel coordinates of the output
(filtered) voxel. Then the value of this voxel is given by the mean
of the input voxels with coordinates xi, yi, and zi for which

((xi - xo) / rx)^2 + ((yi -yo) / ry)^2 + ((zi - zo) / rz)^2 <= 1.

That is, we average over the input voxels that lie in the ellipsoid
centered on the location of the output voxel that is aligned along
the x, y, and z directions and has axes of (half) lengths rx, ry,
and rz.

(You can find this in the createKernelEllipsoid() method of

Thanks, mm


Thank you fro your explanation!
I really appreciate :slight_smile:


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