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