First of all, excuse the abstract wording of the title. I don't know the proper term for the concept I want to find, which is part of my problem I guess.
I've got a cloud of points (in my case it's 3d points, but it shouldn't matter). They are placed in such a way that most of them are in a general area, but with groups of outliers. Take this picture as an example:
I would like to find a value that gives me the center point of the big cloud of points, so to speak. That is, an equivalent of the average that isn't affected by the outliers. But there is an important detail: the bigger cloud should be defined as the larger cloud in size, not the cloud with most points. In the sample image, for example, it is possible that one of the clouds in the lower right has a larger number of points than the large cloud in the left, yet the one in the left should be the chosen cloud.
The problem is that I don't know first hand how many outliers there will be or how far they are going to be from each other, so it's hard to define which points will "form a cloud".
The reason for my question is that I'm basically trying to center a 3d model in a computer application. Using just the denser area isn't valid, since it could represent just a small object that's modeled with high accuracy due to being round.