Is there some code that can automatically take some small set of points (worse, possibly with some noise? You did mention smoothing) and know what volumetric object they came from? Of course not.
Conside 8 points that form the vertices of a cube. Oh. Wait. Are these just 8 points in a specific configuration on the surface of a sphere? You cannot know which object they came from, as it is completely ambiguous.
You might consider computing the convex hull, or perhaps a delaunay tessellation, then ask if the triangulation is topologically equivelent to that of a dissection of a cube. (Note there are two distinct ways to dissect a 3-cube into simplexes, one with 6 pieces, one with 5., and then we would also have rotations thereof.) You could build in some pattern recognition intelligence that would recognize a tessellation as conformable to a cube/hyper-rectangle. But all of this would take some serious understanding of pattern recognition techniques. And it still would be unable to understand the points really just came from a sphere or ellipsoid anyway.
The human eye/brain is great at recognizing things from scattered data. In fact, we see this every night when we look at the night sky and see constellations. But must I point out that even those constellations are highly ambiguous? Two different people can look at the same configuarations and see totally different objects. And they both might be correct! Where is my MC Escher print when I need it?
