  Locating the center of convex objects is important in both image processing
and unsupervised machine learning/data clustering fields. The automated
analysis of biological images uses both of these fields for locating cell
nuclei and for discovering new biological effects or cell phenotypes. In this
work, we develop a novel clustering method for locating the centers of
overlapping convex objects by modeling particles that interact by a short-range
attractive and long-range repulsive potential and are confined to a potential
well created from the data. We apply this method to locating the centers of
clumped nuclei in cultured cells, where we show that it results in a
significant improvement over existing methods (8.2% in F$_1$ score); and we
apply it to unsupervised learning on a difficult data set that has rare classes
without local density maxima, and show it is able to well locate cluster
centers when other clustering techniques fail.
