ABSTRACT

This book provides an accessible yet rigorous introduction to topology and homology focused on the simplicial space. It presents a compact pipeline from the foundations of topology to biomedical applications. It will be of interest to medical physicists, computer scientists, and engineers, as well as undergraduate and graduate students interested in this topic.

Features:

  • Presents a practical guide to algebraic topology as well as persistence homology
  • Contains application examples in the field of biomedicine, including the analysis of histological images and point cloud data

section I|1 pages

Theoretical foundations

chapter Chapter 1|48 pages

Elements of topology and homology

chapter Chapter 2|6 pages

Persistent homology of images

section II|1 pages

Case studies

chapter Chapter 3|6 pages

Recognizing noise

chapter Chapter 4|10 pages

Image segmentation

chapter Chapter 5|5 pages

Point cloud characterization