Algebraic Curves in Multiple-View Geometry | An algebraic geometry approach to computer vision

Jeremy-Yrmeyahu Kaminski

ISBN 10: 3845421320 / ISBN 13: 9783845421322

Published by LAP LAMBERT Academic Publishing, 2011

About this Item

Algebraic Curves in Multiple-View Geometry | An algebraic geometry approach to computer vision | Jeremy-Yrmeyahu Kaminski | Taschenbuch | 92 S. | Englisch | 2011 | LAP LAMBERT Academic Publishing | EAN 9783845421322 | Verantwortliche Person für die EU: OmniScriptum GmbH & Co. KG, Bahnhofstr. 28, 66111 Saarbrücken, info[at]akademikerverlag[dot]de | Anbieter: preigu.

Seller Inventory # 106696503

Bibliographic Details

• Title: Algebraic Curves in Multiple-View Geometry | An algebraic geometry approach to computer vision
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2011
• Language: English
• ISBN 10: 3845421320
• ISBN 13: 9783845421322
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 7D millimeters 220 millimeters width by 150 millimeters height by 7 millimeters depth
• Weight: 155 grams
• Seller catalogs:
  • Bücher

About this title

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.

About the Author

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.