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Tumor segmentation in whole-slide images of histology slides is an importantstep towards computer-assisted diagnosis. In this work, we propose a tumorsegmentation framework based on the novel concept of persistent homologyprofiles (PHPs). For a given image patch, the homology profiles are derived byefficient computation of persistent homology, which is an algebraic tool fromhomology theory. We propose an efficient way of computing topologicalpersistence of an image, alternative to simplicial homology. The PHPs aredevised to distinguish tumor regions from their normal counterparts by modelingthe atypical characteristics of tumor nuclei. We propose two variants of ourmethod for tumor segmentation: one that targets speed without compromisingaccuracy and the other that targets higher accuracy. The fast version is basedon the selection of exemplar image patches from a convolution neural network(CNN) and patch classification by quantifying the divergence between the PHPsof exemplars and the input image patch. Detailed comparative evaluation showsthat the proposed algorithm is significantly faster than competing algorithmswhile achieving comparable results. The accurate version combines the PHPs andhigh-level CNN features and employs a multi-stage ensemble strategy for imagepatch labeling. Experimental results demonstrate that the combination of PHPsand CNN features outperforms competing algorithms. This study is performed ontwo independently collected colorectal datasets containing adenoma,adenocarcinoma, signet and healthy cases. Collectively, the accurate tumorsegmentation produces the highest average patch-level F1-score, as comparedwith competing algorithms, on malignant and healthy cases from both thedatasets. Overall the proposed framework highlights the utility of persistenthomology for histopathology image analysis.

Fast and Accurate Tumor Segmentation of Histology Images using Persistent Homology and Deep Convolutional Features