graphics3d – How to add and remove Gaussian noise on a set of vertices of 3D objects?

I have tried the following:
NoisyVertices = # + RandomReal[NormalDistribution[0, Sqrt[0.02]]]& / @ vertices;

Now that I have noisy peaks, how can I remove noise in order to get an approximation of the original vertices, I found GaussianFilter[] but I do not understand how to apply it to get the filtered coordinates.