Algebraic Curves in Multiple-View Geometry: An algebraic geometry approach to computer vision - Couverture souple

Kaminski, Jeremy-Yrmeyahu

 
9783845421322: Algebraic Curves in Multiple-View Geometry: An algebraic geometry approach to computer vision
Couverture souple
ISBN 10 : 3845421320 ISBN 13 : 9783845421322
Editeur : LAP LAMBERT Academic Publishing, 2011

Synopsis

We introduce multiple-view geometry for algebraic curves,with applications in both static and dynamic scenes. More precisely, we show how the epipolar geometry can be recovered from algebraic curves. For that purpose, we introduce a generalization of Kruppa’s equations, which express the epipolar constraint for algebraic curves. Reconstruction from a single image based on symmetry is also considered and we show how this relates to algebraic curves for a simple example. We also investigate the question of three-dimensional reconstruction of an algebraic curve from two or more views. In the case of two views, we show that for a generic situation, there are two solutions for the reconstruction, which allows extracting the right solution, provided the degree of the curve is greater or equal to 3. When more than two views are available,we show that there construction can be done by linear computations, using either the dual curve or the variety of intersecting lines. In both cases, no curve fitting is necessary in the image space. Finally we focus on dynamic scenes and show when and how the trajectory of a moving point can be recovered from a moving camera.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

We introduce multiple-view geometry for algebraic curves,with applications in both static and dynamic scenes. More precisely, we show how the epipolar geometry can be recovered from algebraic curves. For that purpose, we introduce a generalization of Kruppa’s equations, which express the epipolar constraint for algebraic curves. Reconstruction from a single image based on symmetry is also considered and we show how this relates to algebraic curves for a simple example. We also investigate the question of three-dimensional reconstruction of an algebraic curve from two or more views. In the case of two views, we show that for a generic situation, there are two solutions for the reconstruction, which allows extracting the right solution, provided the degree of the curve is greater or equal to 3. When more than two views are available,we show that there construction can be done by linear computations, using either the dual curve or the variety of intersecting lines. In both cases, no curve fitting is necessary in the image space. Finally we focus on dynamic scenes and show when and how the trajectory of a moving point can be recovered from a moving camera.

Biographie de l'auteur

Jeremy Y. Kaminski received a M.Sc. degree from Paris-Orsay university and graduated Ecole des Mines de Paris. He graduated his Ph.D. from The Hebrew University of Jerusalem. He is currently an assistant professor at Holon Institute of Technology. His research interests includes applied algebraic geometry, computer vision and computer algebra.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2011
Langue
anglais
ISBN 10 
3845421320
ISBN 13 
9783845421322
Reliure
Broché
Nombre de pages
92
Coordonnées du fabricant
non disponible
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