C++ recognize shape from points

I'am trying to find out an algorithm to recognize circle in array of points.

Lets say that I've got points array where circle could or could not be stored (that also means array doesn't have to store only circle's points, there could be some "extra" points before or after circle's data).

I've already tried some algorithms but none of them work properly with those "extra" points. Have you got any ideas how to deal with this problem?