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Ricci Flow for Shape Analysis and Surface Registration

Theories, Algorithms and Applications

  • Book
  • © 2013

Overview

Authors:
  1. Wei Zeng

    1. Computing and Information Science, Florida International University, Miami, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Xianfeng David Gu

    1. Computer Science, State University of New York, Stony Brook, USA

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    You can also search for this author in PubMed   Google Scholar

  • Presents Ricci flow analysis in a simplified discrete setting
  • Illustrates applications from engineering and medicine that represent state-of-the-art and new exciting challenges
  • Written by experts in the field
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Wei Zeng, Xianfeng David Gu
    Pages 1-15

  3. Surface Topology and Geometry

    • Wei Zeng, Xianfeng David Gu
    Pages 17-30

  4. Riemann Surface

    • Wei Zeng, Xianfeng David Gu
    Pages 31-58

  5. Discrete Surface Ricci Flow

    • Wei Zeng, Xianfeng David Gu
    Pages 59-100

  6. Algorithms and Applications

    • Wei Zeng, Xianfeng David Gu
    Pages 101-136

  7. Back Matter

    Pages 137-139
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Keywords

About this book

​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 adapt the Ricci 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 book is accessible to engineers and medical experts, including educators, researchers, students and industry engineers who have an interest in solving real problems related to shape analysis and surface registration.  

Reviews

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)

Authors and Affiliations

  • Computing and Information Science, Florida International University, Miami, USA

    Wei Zeng

  • Computer Science, State University of New York, Stony Brook, USA

    Xianfeng David Gu

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