I have a cloud of 3D points. I want to find the centroid of the "densest region", meaning I want to find a close approximation to the location of the maximum value of the convolution of the point cloud with a spherical Gaussian of scale σ (where σ is chosen appropriately so that there is only one clear global maximum in the convolution, corresponding to some intuitive notion of "densest region" and centrality, relative to the distribution of points).
I assume I can estimate the solution using something like RANSAC applied to a centroid calculation, to discard outliers? Or is there a better or more robust or efficient way to find the centroid of the point cloud, in a way that is insensitive to outliers?