Segmentation of biomedical images based on a computational topology framework

The homology groups of a topological space provide us with information about its connectivity and the number and type of holes in it. This type of information can find practical applications in describing the intrinsic structure of an image, as well as in identifying equivalence classes in collections of images. When computing homological characteristics, the existence and strength of the relationships between each pair of points in the topological space are studied. The practical use of this approach begins by building a topological space from the image, in which the computation of the homology groups can be carried out in a feasible time. Once the homological properties are obtained, what follows is the task of translating such information into operations such as image segmentation. This work presents a technique for denoising persistent diagrams and reconstructing the shape of segmented objects using the remaining classes on the diagram. A case study for the segmentation of cell nuclei in histological images is used for demonstration purposes. With this approach: a) topological denoising is achieved by aggregating trivial classes on the persistence diagram, and b) a growing seed algorithm uses the information obtained during the construction of the persistence diagram for the reconstruction of the segmented cell structures.