Bronstein, Alexander M.; Bronstein, Michael M.; Kimmel, Ron Numerical geometry of non-rigid shapes. (English) Zbl 1178.68608 Monographs in Computer Science. New York, NY: Springer (ISBN 978-0-387-73300-5/hbk). xxi, 340 p. (2008). The first two chapters are dedicated to the mathematical background of the book’s topic. Since the authors’ model of a non-rigid world stands on three pillars: metric geometry, discrete geometry, and numerical optimization, the review of the mathematical background touches these areas. Chapter 3 and Chapter 4 present the geometric foundations through the glasses of the computer scientist, who has to convert the continuous geometric space into discrete objects tractable by a computer. In Chapter 4 the authors present the fast marching, a class of efficient numerical algorithms for geodesic distance measurement. Numerical optimization is presented in Chapter 5. Chapter 6 is the first chapter where the applications appear. The authors’ emphasis in this chapter is on iterative closest point algorithms, a class of numerical methods for rigid object comparison and matching. In Chapters 7, 8, and 9 the authors describe the ways of creating deformation-invariant representations of non-rigid shapes. Chapter 10 is devoted to the problem of shape similarity. In Chapter 11 the authors discuss partial similarity, the problem of comparing shapes having similar parts. Chapter 12 deals with the problem of correspondence between non-rigid shapes. Chapter 13 presents a face recognition system to demonstrate and summarize the tools discussed in this book. Finally, the last chapter gives a short retrospective and concludes the book. Reviewer: Attila Fazekas (Debrecen) Cited in 50 Documents MSC: 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) 68-02 Research exposition (monographs, survey articles) pertaining to computer science 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry Keywords:discrete geometry; face recognition system × Cite Format Result Cite Review PDF Full Text: DOI