We consider the problem of automated cancer diagnosis in the context of breast tissues. We present graph theoretical techniques that identify and compute quantitative metrics for tissue characterization and classification. We segment digital images of histopatological tissue samples using k-means algorithm. For each segmented image we generate different cell-graphs using positional coordinates of cells and surrounding matrix components. These cell-graphs have 500-2000 cells(nodes) with 1000-10000 links depending on the tissue and the type of cell-graph being used. We calculate a set of global metrics from cell-graphs and use them as the feature set for learning. We compare our technique, hierarchical cell graphs, with other techniques based on intensity values of images, Delaunay triangulation of the cells, the previous technique we proposed for brain tissue images and with the hybrid approach that we introduce in this paper. Among the compared techniques, hierarchical-graph approach gives 81.8% accuracy whereas we obtain 61.0%, 54.1% and 75.9% accuracy with intensity-based features, Delaunay triangulation and our previous technique, respectively.

This work reports a novel computational method based on augmented cell-graphs (ACG), which are constructed from low-magnification tissue images for the mathematical diagnosis of brain cancer (malignant glioma). An ACG is a simple, undirected, weighted and complete graph in which a node represents a cell cluster and an edge between a pair of nodes defines a binary relationship between them. Both the nodes and the edges of an ACG are assigned weights to capture more information about the topology of the tissue. In this work, the experiments are conducted on a dataset that is comprised of 646 human brain biopsy samples from 60 different patients. It is shown that the ACG approach yields sensitivity of 97.53% and specificities of 93.33 and 98.15% (for the inflamed and healthy, respectively) at the tissue level in glioma diagnosis.

Abstract-This work presents a graph-based representation (a.k.a., cell-graph) of histopathological images for automated cancer diagnosis by probabilistically assigning a link between a pair of cells (or cell clusters). Since the node set of a cell-graph can include a cluster of cells as well as individual ones, it enables working with low-cost, low-magnification photomicrographs. The contributions of this work are twofold. First, it is shown that without establishing a pairwise spatial relation between the cells (i.e., the edges of a cellgraph), neither the spatial distribution of the cells nor the texture analysis of the images yields accurate results for tissue level diagnosis of brain cancer called malignant glioma. Second, this work defines a set of global metrics by processing the entire cell-graph to capture tissue level information coded into the histopathological images. In this work, the results are obtained on the photomicrographs of 646 archival brain biopsy samples of 60 different patients. It is shown that the global metrics of cell-graphs distinguish cancerous tissues from noncancerous ones with high accuracy (at least 99 percent accuracy for healthy tissues with lower cellular density level, and at least 92 percent accuracy for benign tissues with similar high cellular density level such as nonneoplastic reactive/inflammatory conditions).

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