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Geometric Methods and Applications
For Computer Science and Engineering
Buch von Jean Gallier
Sprache: Englisch

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Beschreibung

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)

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)

Über den Autor
Jean Gallier is a Professor at the University of Pennsylvania in the Computer and Information Science Department at the School of Engineering and Applied Science.
Zusammenfassung

More examples and references added

Chapters have been expanded

Offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups

Inhaltsverzeichnis

Introduction.- Basics of Affine Geometry.- Basic Properties of Convex Sets.- Embedding an Affine Space in a Vector Space.- Basics of Projective Geometry.- Basics of Euclidean Geometry.- Separating and Supporting Hyperplanes; Polar Duality.- Polytopes and Polyhedra.- The Cartan-Dieudonn¿e Theorem.- The Quaternions and the Spaces S3, SU(2), SO(3), and RP3 .- Dirichlet-Voronoi Diagrams.- Basics of Hermitian Geometry.- Spectral Theorems.- Singular Value Decomposition (SVD) and Polar Form.- Applications of SVD and Pseudo-Inverses.- Quadratic Optimization Problems.- Schur Complements and Applications.- Quadratic Optimization and Contour Grouping.- Basics of Manifolds and Classical Lie Groups.- Basics of the Differential Geometry of Curves.- Basics of the Differential Geometry of Surfaces.- Appendix.- References.- Symbol Index.- IndexAppendix.- References.- Symbol Index.- Index

Details
Erscheinungsjahr: 2011
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 680
Inhalt: xxviii
680 S.
20 s/w Illustr.
ISBN-13: 9781441999603
ISBN-10: 1441999604
Sprache: Englisch
Herstellernummer: 80036164
Einband: Gebunden
Autor: Gallier, Jean
Auflage: 2nd 2011 edition
Hersteller: Springer Nature Singapore
Springer US, New York, N.Y.
Maße: 244 x 169 x 43 mm
Von/Mit: Jean Gallier
Erscheinungsdatum: 21.06.2011
Gewicht: 1,175 kg
preigu-id: 107067752
Über den Autor
Jean Gallier is a Professor at the University of Pennsylvania in the Computer and Information Science Department at the School of Engineering and Applied Science.
Zusammenfassung

More examples and references added

Chapters have been expanded

Offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups

Inhaltsverzeichnis

Introduction.- Basics of Affine Geometry.- Basic Properties of Convex Sets.- Embedding an Affine Space in a Vector Space.- Basics of Projective Geometry.- Basics of Euclidean Geometry.- Separating and Supporting Hyperplanes; Polar Duality.- Polytopes and Polyhedra.- The Cartan-Dieudonn¿e Theorem.- The Quaternions and the Spaces S3, SU(2), SO(3), and RP3 .- Dirichlet-Voronoi Diagrams.- Basics of Hermitian Geometry.- Spectral Theorems.- Singular Value Decomposition (SVD) and Polar Form.- Applications of SVD and Pseudo-Inverses.- Quadratic Optimization Problems.- Schur Complements and Applications.- Quadratic Optimization and Contour Grouping.- Basics of Manifolds and Classical Lie Groups.- Basics of the Differential Geometry of Curves.- Basics of the Differential Geometry of Surfaces.- Appendix.- References.- Symbol Index.- IndexAppendix.- References.- Symbol Index.- Index

Details
Erscheinungsjahr: 2011
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 680
Inhalt: xxviii
680 S.
20 s/w Illustr.
ISBN-13: 9781441999603
ISBN-10: 1441999604
Sprache: Englisch
Herstellernummer: 80036164
Einband: Gebunden
Autor: Gallier, Jean
Auflage: 2nd 2011 edition
Hersteller: Springer Nature Singapore
Springer US, New York, N.Y.
Maße: 244 x 169 x 43 mm
Von/Mit: Jean Gallier
Erscheinungsdatum: 21.06.2011
Gewicht: 1,175 kg
preigu-id: 107067752
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