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Uncertain Projective Geometry [electronic resource] :Statistical Reasoning for Polyhedral Object Reconstruction /

By: Heuel, Stephan [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Computer Science: 3008Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2004.Description: XVIII, 210 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540246565.Subject(s): Mathematics | Mathematical statistics | Artificial intelligence | Computer graphics | Image processing | Pattern recognition | Geometry | Mathematics | Geometry | Pattern Recognition | Image Processing and Computer Vision | Probability and Statistics in Computer Science | Computer Graphics | Artificial Intelligence (incl. Robotics)Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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