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How to efficiently filter out points geometrically close to each other?

I have a list of points from an image, and I have a method to measure the distance between two points.

Is there a more efficient way - than the naive approach - to remove points from that list that are too close (the 2D coordinates) to each other?

I wouldn't like to remove them all, if I had 4 points which were close, I would choose one point to keep and remove the other 3.