Uncertain Projective Geometry - Statistical Reasoning for Polyhedral Object Reconstruction

Algebraic projective geometry, with its multilinear relations and its embedding into Grassmann-Cayley algebra, has become the basic representation of multiple view geometry, resulting in deep insights into the algebraic structure of geometric relations, as well as in efficient and versatile algorithms for computer vision and image analysis.
This book provides a coherent integration of algebraic projective geometry and spatial reasoning under uncertainty with applications in computer vision. Beyond systematically introducing the theoretical foundations from geometry and statistics and clear rules for performing geometric reasoning under uncertainty, the author provides a collection of detailed algorithms.
The book addresses researchers and advanced students interested in algebraic projective geometry for image analysis, in statistical representation of objects and transformations, or in generic tools for testing and estimating within the context of geometric multiple-view analysis.

List of contents

1 Introduction.- 2 Representation of Geometric Entities and Transformations.- 3 Geometric Reasoning Using Projective Geometry.- 4 Statistical Geometric Reasoning.- 5 Polyhedral Object Reconstruction.- 6 Conclusions.- A Notation.- B Linear Algebra.- C Statistics.

Summary

Algebraic projective geometry, with its multilinear relations and its embedding into Grassmann-Cayley algebra, has become the basic representation of multiple view geometry, resulting in deep insights into the algebraic structure of geometric relations, as well as in efficient and versatile algorithms for computer vision and image analysis.
This book provides a coherent integration of algebraic projective geometry and spatial reasoning under uncertainty with applications in computer vision. Beyond systematically introducing the theoretical foundations from geometry and statistics and clear rules for performing geometric reasoning under uncertainty, the author provides a collection of detailed algorithms.
The book addresses researchers and advanced students interested in algebraic projective geometry for image analysis, in statistical representation of objects and transformations, or in generic tools for testing and estimating within the context of geometric multiple-view analysis.

Product details

• Authors: S. Heuel, Stephan Heuel
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 20.07.2004
• EAN: 9783540220299
• ISBN: 978-3-540-22029-9
• No. of pages: 210
• Weight: 352 g
• Illustrations: XVIII, 210 p.
• Series: Lecture Notes in Computer Science; Lecture Notes in Computer Science
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; C, Künstliche Intelligenz, Artificial Intelligence, Mustererkennung, Wahrscheinlichkeitsrechnung und Statistik, Grafikprogrammierung, Maschinelles Sehen, Bildverstehen, Mathematik für Informatiker, computer science, geometry, Computer Vision, Image Processing and Computer Vision, Computer Graphics, pattern recognition, Mathematical & statistical software, Automated Pattern Recognition, Maths for computer scientists, Mathematical statistics, Probability and Statistics in Computer Science, Optical data processing, Image processing, Graphics programming