Ricci Flow for Shape Analysis and Surface Registration: Theories, Algorithms and Applications

ISBN-13: 9781461487807 / Angielski / Miękka / 2013 / 139 str.

Wei Zeng; Xianfeng David Gu

Opis

Ricci Flow for Shape Analysis and Surface Registration introduces the beautiful and profound Ricci flow theory in a discrete setting. By using basic tools in linear algebra and multivariate calculus, readers can deduce all the major theorems in surface Ricci flow by themselves. The authors adapttheRicci flow theory to practical computational algorithms, apply Ricci flow for shape analysis and surface registration, and demonstrate the power of Ricci flow in many applications in medical imaging, computer graphics, computer vision and wireless sensor network. Due to minimal pre-requisites, this bookis accessible toengineersand medicalexperts, including educators, researchers, students and industry engineerswhohave an interest insolvingreal problems related to shape analysis and surface registration.

Recenzje

From the book reviews:

"The book is aimed at providing mathematical foundations and algorithms for practitioners, especially engineers ... One of the most fascinating parts of the book consists of the applications of discrete Ricci flow pioneered by the authors. ... The authors have developed very effective methods of computing the solutions of discrete Ricci flow and have applied them successfully to solve many real world imaging problems." (Bennett Chow, David Glickenstein and Feng Luo, Bulletin of the American Mathematical Society, Vol. 54 (1), January, 2017)

"It provides both theoretical foundations and computational methods for surface Ricci flow, and describes its applications in surface registration and shape analysis. ... This monograph is addressed mainly to graduate students and researchers in the fields of computer science, applied mathematics, engineering, and medical imaging. The book is recommended as well for professionals in the fields related to surface registration and shape analysis ... ." (Vladimir Balan, Mathematical Reviews, June, 2014)

Spis treści

1. Introduction.- 2. Computational.- 3. Computational Geometry.- 4. Differential Geometry of Surface.- 5. Riemann Surface.- 6. Ricci Flow.- 7. Topological Algorithms.- 8. Harmonic Maps.- 9. Discrete Ricci Flow.- 10. Shape Analysis.- 11. Surface Diffeomorphism.- 12. Medical Imaging  Applications.- 13. Computer Vision Applications.- 14. Computer Graphics Applications.- 15. Network Applications.​