Suggestions for denoising point cloud

Hello guys, I have a question about point clouds, so I'll just jump straight into it. I have a point cloud of an object made from a matrix of points.

points = [x; y; z]

I read this in and display with a scatter. The result is the picture I have attached. I get noise introduced by the method of acquisition (I am using a stereo vision technique). You can see the small unwanted clusters and singular points in the image.

I would really appreciate suggestions on how to remove [the majority] of this noise. I have been using a standard deviation distance and a median absolute deviation technique that were suggested to me in a previous question, but I am still left with a lot of these unwanted points. I wonder if there is a way to target small clusters of points that are not part of the main concentration.

I realize this could be a complex one, so any pointers at all would be very, very welcome.

Thanks in advance guys