E-Book Overview
This book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, robotics, or machine learning.
This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal component analysis, manifolds and Lie groups, quadratic optimization, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presented in this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics.
In this extensively updated second edition, more material on convex sets, Farkas’s lemma, quadratic optimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now includes a presentation of PCA.
The book is well illustrated and has chapter summaries and a large number of exercises throughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers.
Reviews of first edition:
"Gallier's book will be a useful source for anyone interested in applications of geometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications." (Mathematical Reviews, 2001)
"...it will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry." (The Australian Mathematical Society, 2001)
E-Book Content
Texts in Applied Mathematics 38 Editors S. Antman P. Holmes L. Sirovich K.R. Sreenivasan Advisors G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton For other volumes published in this series, go to www.springer.com/series/1214 Jean Gallier Geometric Methods and Applications For Computer Science and Engineering Second Edition Jean Gallier University of Pennsylvania Department of Computer and Information Science 3330 Walnut Street Philadelphia, PA 19104 USA
[email protected] Series Editors S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA
[email protected] P. Holmes Department of Mechanical and Aerospace Engineering Princeton University 215 Fine Hall Princeton, NJ 08544
[email protected] L. Sirovich Laboratory of Applied Mathematics Department of Biomathematical Sciences Mount Sinai School of Medicine New York, NY 10029-6574
[email protected] K.R. Sreenivasan Department of Physics New York University 70 Washington Square South New York City, NY 10012
[email protected] ISSN 0939-2475 ISBN 978-1-4419-9960-3 e-ISBN 978-1-4419-9961-0 DOI 10.1007/978-1-4419-9961-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Num