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Clinical pathology relies on manual compartmentalization and quantification of biological structures, which is time
consuming and often error-prone. Application of computer vision segmentation algorithms to histopathological image
analysis, in contrast, can offer fast, reproducible, and accurate quantitative analysis to aid pathologists. Algorithms tunable
to different biologically relevant structures can allow accurate, precise, and reproducible estimates of disease states. In this
direction, we have developed a fast, unsupervised computational method for simultaneously separating all biologically
relevant structures from histopathological images in multi-scale. Segmentation is achieved by solving an energy
optimization problem. Representing the image as a graph, nodes (pixels) are grouped by minimizing a Potts model
Hamiltonian, adopted from theoretical physics, modeling interacting electron spins. Pixel relationships (modeled as edges)
are used to update the energy of the partitioned graph. By iteratively improving the clustering, the optimal number of
segments is revealed. To reduce computational time, the graph is simplified using a Cantor pairing function to intelligently
reduce the number of included nodes. The classified nodes are then used to train a multiclass support vector machine to
apply the segmentation over the full image. Accurate segmentations of images with as many as 106 pixels can be completed
only in 5 sec, allowing for attainable multi-scale visualization. To establish clinical potential, we employed our method in
renal biopsies to quantitatively visualize for the first time scale variant compartments of heterogeneous intra- and extraglomerular
structures simultaneously. Implications of the utility of our method extend to fields such as oncology,
genomics, and non-biological problems.
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