How to view the boundary of a set

I have defined a set in 3D space as a structured grid, where the value in each cell is either 0 or 1. I would like to view the boundary of this set. So I use the Contour filter. But this gives a very bumpy boundary, and I would like to smooth it out.

For example, suppose the set is a sphere. So there cell takes the value 1 if x^2+y^2+z^2 < 9, and takes the value 0 otherwise. You would think that the a contour at the value 0.5 would give a good rendition of a sphere. But paraview will give a “lego” style rendition, because it doesn’t know that this is not what I want.

Are there any filters that can help me in this regard? I am very new to paraview, so this may be a very standard question. But I don’t even know which keywords to feed into google.

As you work with cell data, you extract cells and see cells as they are in a structured grid, i.e as ‘lego’.
You may want to work with point data so the extraction will extract points and recompute surface to have a smooth render.

You can easily test by using CellDataToPointData filter before extracting the boundary.