  Unsupervised segmentation of large images using a Potts model Hamiltonian is
unique in that segmentation is governed by a resolution parameter which scales
the sensitivity to small clusters. Here, the input image is first modeled as a
graph, which is then segmented by minimizing a Hamiltonian cost function
defined on the graph and the respective segments. However, there exists no
closed form solution of this optimization, and using previous iterative
algorithmic solution techniques, the problem scales quadratically in the Input
Length. Therefore, while Potts model segmentation gives accurate segmentation,
it is grossly underutilized as an unsupervised learning technique. We propose a
fast statistical down-sampling of input image pixels based on the respective
color features, and a new iterative method to minimize the Potts model energy
considering pixel to segment relationship. This method is generalizable and can
be extended for image pixel texture features as well as spatial features. We
demonstrate that this new method is highly efficient, and outperforms existing
methods for Potts model based image segmentation. We demonstrate the
application of our method in medical microscopy image segmentation;
particularly, in segmenting renal glomerular micro-environment in renal
pathology. Our method is not limited to image segmentation, and can be extended
to any image/data segmentation/clustering task for arbitrary datasets with
discrete features.
