Overview

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

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9781138336346

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In writing Computational Topology for Biomedical Images and Data: Theory and Applications, the interdisciplinary collaboration among Rodrigo R. Moraleda, Nektarios A. Valous, Wei Xiong, and Niels Halama has produced a work that will hold its own ground for a variety of reasons. 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 fulfil - 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...As topological methods have only recently started finding application in the analysis of biomedical data, the book makes a timely entry in the market. A data-centric approach has allowed the book to showcase the relevance and impact of esoteric theories on real-world problems. The book is clear in its mandate of defining a target audience, namely the biomedical community...The book targets a selected audience but may be impactful in fields beyond its defined scope. Despite the evident focus of the book on biomedical data, the right audience includes individuals interested in data analysis across disciplines, and at all stages-from beginners to experts. Seasoned researchers in the field of applied and computational topology will find it a convenient reference manual....The book successfully brings together disciplines that rarely interact and is a glowing testimony to the impact of interdisciplinary collaborations. The symbiotic effort of a number of specialists in different areas has brought forth a creation that is complete in its demonstration of the relevance of abstract mathematical ideas in gaining deeper understanding of concrete real-life problems. The interdisciplinary expertise of the authors is evident in the deft selection and subsequent integration of cross disciplinary components in a seamless fashion. 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. - Pratyush Pranav, Centre de Recherche Astrophysique de Lyon, Ecole Normale Superieure de Lyon, in IEEE SIGNAL PROCESSING MAGAZINE, July 2021

In writing Computational Topology for Biomedical Images and Data: Theory and Applications, the interdisciplinary collaboration among Rodrigo R. Moraleda, Nektarios A. Valous, Wei Xiong, and Niels Halama has produced a work that will hold its own ground for a variety of reasons. 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 fulfil - 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...As topological methods have only recently started finding application in the analysis of biomedical data, the book makes a timely entry in the market. A data-centric approach has allowed the book to showcase the relevance and impact of esoteric theories on real-world problems. The book is clear in its mandate of defining a target audience, namely the biomedical community...The book targets a selected audience but may be impactful in fields beyond its defined scope. Despite the evident focus of the book on biomedical data, the right audience includes individuals interested in data analysis across disciplines, and at all stages-from beginners to experts. Seasoned researchers in the field of applied and computational topology will find it a convenient reference manual....The book successfully brings together disciplines that rarely interact and is a glowing testimony to the impact of interdisciplinary collaborations. The symbiotic effort of a number of specialists in different areas has brought forth a creation that is complete in its demonstration of the relevance of abstract mathematical ideas in gaining deeper understanding of concrete real-life problems. The interdisciplinary expertise of the authors is evident in the deft selection and subsequent integration of cross disciplinary components in a seamless fashion. 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. - Pratyush Pranav, Centre de Recherche Astrophysique de Lyon, Ecole Normale Superieure de Lyon, in IEEE SIGNAL PROCESSING MAGAZINE, July 2021 In writing Computational Topology for Biomedical Images and Data: Theory and Applications, the interdisciplinary collaboration among Rodrigo R. Moraleda, Nektarios A. Valous, Wei Xiong, and Niels Halama has produced a work that will hold its own ground for a variety of reasons. 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 fulfil - 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...As topological methods have only recently started finding application in the analysis of biomedical data, the book makes a timely entry in the market. A data-centric approach has allowed the book to showcase the relevance and impact of esoteric theories on real-world problems. The book is clear in its mandate of defining a target audience, namely the biomedical community...The book targets a selected audience but may be impactful in fields beyond its defined scope. Despite the evident focus of the book on biomedical data, the right audience includes individuals interested in data analysis across disciplines, and at all stages-from beginners to experts. Seasoned researchers in the field of applied and computational topology will find it a convenient reference manual....The book successfully brings together disciplines that rarely interact and is a glowing testimony to the impact of interdisciplinary collaborations. The symbiotic effort of a number of specialists in different areas has brought forth a creation that is complete in its demonstration of the relevance of abstract mathematical ideas in gaining deeper understanding of concrete real-life problems. The interdisciplinary expertise of the authors is evident in the deft selection and subsequent integration of cross disciplinary components in a seamless fashion. 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. - Pratyush Pranav, Centre de Recherche Astrophysique de Lyon, Ecole Normale Superieure de Lyon, in IEEE SIGNAL PROCESSING MAGAZINE, July 2021

Author Information

Rodrigo Rojas Moraleda obtained his PhD in computer science from Federico Santa María Technical University, Chile. He has research experience in the fields of computational biomedicine and applied mathematics. His current affiliation is with the German Cancer Research Center and the National Center for Tumor Diseases Heidelberg, Germany. Nektarios A. Valous obtained his PhD in biosystems engineering from University College Dublin, Ireland. He has research experience in the fields of computational biomedicine and interdisciplinary physics. His current affiliation is with the German Cancer Research Center and the National Center for Tumor Diseases Heidelberg, Germany. Wei Xiong obtained her PhD in mathematics from Heidelberg University, Germany. She has worked in the statistical physics and theoretical biophysics group (Institute for Theoretical Physics) and has research experience in the fields of computational mathematics and scientific computing. Her current affiliation is with the Institute for Theoretical Physics in Heidelberg University, Germany. Niels Halama is the head of the department of translational immunotherapy in the German Cancer Research Center, Germany. He has research experience in the fields of cancer immunology and computational biomedicine. His current affiliation is with the German Cancer Research Center and the National Center for Tumor Diseases Heidelberg, Germany.

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