ABSTRACT
The chapter presents a computational topology implementation in the context of segmenting cell nuclei from histological images. The proposed approach is carried out in the following steps:
An external process retrieves digital images from a database. In digital pathology, these images often consist of digitized glass slides known as whole-slide images.
A change in the color model is carried out in order to create a feature space that captures well the properties of the region-of-interest (ROI), e.g., cell nuclei. A feature space is sought where the persistent homology of the ROIs is different from the persistent homology of other structures in the image.
Images are deconstructed into connected components at different scales.
An inclusion tree is built that stores information between connected components.
Persistent homology is used to summarize the Betti number dimension-0 changes when step (iv) occurs.
Standard statistical methods are used to define a confidence interval for the birth and death of homological classes. In many cases, this interval is enough to identify an ROI in the image which makes it a kind of topological signature.
Segmentation masks are obtained; this is a post-processing step for transforming selected points over the persistent diagram into a binary mask.
