Uncertain Projective Geometry: Statistical Reasoning for Polyhedral Object Reconstruction

Stephan Heuel (auth.)3540220291, 9783540220299, 9783540246565

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.

Table of contents :
Front Matter….Pages –
1 Introduction….Pages 1-17
2 Representation of Geometric Entities and Transformations….Pages 19-45
3 Geometric Reasoning Using Projective Geometry….Pages 47-95
4 Statistical Geometric Reasoning….Pages 97-148
5 Polyhedral Object Reconstruction….Pages 149-172
6 Conclusions….Pages 173-177
A Notation….Pages 179-181
B Linear Algebra….Pages 183-185
C Statistics….Pages 187-195
Back Matter….Pages –