Computational Topology for Biomedical Images and Data: Theory and Applications [Book Review]

This is a classic textbook on computational topology. Big data or data analysis, of which topological data analysis is a major component, is a burgeoning field at the moment. A foray into “big data” quickly brings to front two of the central statistical challenges of our times— detection and classification of structure in extremely large, high-dimensional, data sets. Among the most intriguing new approaches to this challenge is topological data analysis (TDA), the primary aim of which is providing topologically informative preanalyses of data, which serve as input to more quantitative analyses at a later stage. The most enticing aspect of the book is the successful rendezvous between compactness and completeness. While the compactness does not allow it to cover the entire breadth of topics relevant to the field of computational topology, it is an excellent choice for the mandate that the book aspires to fulfill—introduction of computational topology as a potentially powerful tool for diagnostics associated with biomedical images and data. The completeness is reflected in a prudent selection, and rigorous treatment of the background mathematical concepts, essential toward building a functional data analysis pipeline based on tools from computational topology. The authors have achieved a fine balance between theory and application, and the book is a pleasure to read. The book will definitely be a frequently used and a cherished item in my personal collection. Due to the breadth in the topics covered, compactness and lucidity, it is my hope and belief that the book will quickly find itself on the shelves of students and early researchers in TDA as a must-have, yet at the same time serve as a frequent go-to reference manual for faculty and seasoned researchers.