Meet Taubin smoothing. It is a nice smoothing method that is great for smoothing voxel based meshes. So for smoothing stepped "Lego-like" meshes.

The left here shows a raw voxelised (thresholded) voxel boundary surface. On the right is the Taubin smoothed result.

Taubin smoothing works by first doing an aggressive Laplacian smoothing step (a bit like a blurring), which removes bumps etc, but which unfortunately can distort the shape too (e.g. unwanted shrinkage/growth). Next it uses an "inverse smooth" (a bit like a sharpening operation) to attempt to push back the shape a bit to avoid distortion. With the right parameter choices it can perform really well.

This animation is for a thresholded 3D image. The colors are the original voxel intensities. The resulting shape presents as a central sphere like blob contained in a dodecahedron "cage".

See also: https://doi.org/10.1145/218380.218473

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