IMAGE SEGMENTATION CONSTRAINED BY TOPOLOGICAL INVARIANTS FOR DIGITAL PATHOLOGY

Abstract

The subject of this thesis is situated in the field of invariants pattern recognition methodsfor image analysis. This thesis aim to formulate a method to segment regions of interest(ROIs) across large sets of non-labeled histological digital images. The achievement of animage segmentation method capable of generalizing its results beyond particular samplesrepresents a major challenge for computer engineering demanded in applications meantto be used in real-world environments.In recent years, algebraic topology, a field of mathematics, has established a robustand versatile way to obtain qualitative information from data. The most fundamentalqualitative description of an object is given by the study of its topology, how the objectis connected, how many holes it has, and of what type. That allows to characterizedata sets according to their structure, increasing our understanding of their properties.Specifically, in this thesis, we explore how such topological information can be gatheredfrom discrete 2D images. To obtain topological information from a digital space, e.g.,Z2, which is used to model computer images, we resort to coarsening the image data.We do this through morphological transformations at multiple resolutions that resultin a sequence of connected components configurations. We characterize the underlyingtopology of the image by studying how the topology varies through that sequence. Weinvestigate whether such a topological characterization can be used as a feature for thetask of image segmentation. We consider both the theoretical and computational aspectsof our topological approach for ROI segmentation. Regarding the second, the domain ofapplication of this work is digital pathology, in particular, whole-slides imaging (WSI).WSI works with high-resolution digital images obtained from histological glass slides.The digitization of glass slides is susceptible to mistakes and abnormalities in tissuepreparation or parameters of microscopy, leading to artifacts. In this thesis, we show,through numerical results, that topology allows us to obtain a compact image representation,discriminative enough for obtaining effciently robust segmentations in scenariosof data variance and noise, common issues in digital pathology.