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Unsupervised segmentation of large images using a Potts model Hamiltonian isunique in that segmentation is governed by a resolution parameter which scalesthe sensitivity to small clusters. Here, the input image is first modeled as agraph, which is then segmented by minimizing a Hamiltonian cost functiondefined on the graph and the respective segments. However, there exists noclosed form solution of this optimization, and using previous iterativealgorithmic solution techniques, the problem scales quadratically in the InputLength. Therefore, while Potts model segmentation gives accurate segmentation,it is grossly underutilized as an unsupervised learning technique. We propose afast statistical down-sampling of input image pixels based on the respectivecolor features, and a new iterative method to minimize the Potts model energyconsidering pixel to segment relationship. This method is generalizable and canbe extended for image pixel texture features as well as spatial features. Wedemonstrate that this new method is highly efficient, and outperforms existingmethods for Potts model based image segmentation. We demonstrate theapplication of our method in medical microscopy image segmentation;particularly, in segmenting renal glomerular micro-environment in renalpathology. Our method is not limited to image segmentation, and can be extendedto any image/data segmentation/clustering task for arbitrary datasets withdiscrete features.

Unsupervised Community Detection with a Potts Model Hamiltonian, an Efficient Algorithmic Solution, and Applications in Digital Pathology