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Lecture Notes in Mathematics

Local Features in Natural Images via Singularity Theory

Authors: Damon, James, Giblin, Peter, Haslinger, Gareth

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  • Includes geometric features of objects, shade/shadow features, and apparent contours
  • Analyzes generic changes under viewer movement
  • Amply illustrated with computer generated images 
  • Yields approach for edge detection where multiple curves meet
  • Employs singularity theory on semi-analytic stratified spaces
  • Combines singularity methods with geometry of surfaces
  • Builds on earlier results in singularity theory and shows necessity of
  • topological methods
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About this book

This monograph considers a basic problem in the computer analysis of natural images, which are images of scenes involving multiple objects that are obtained by a camera lens or a viewer’s eye. The goal is to detect geometric features of objects in the image and to separate regions of the objects with distinct visual properties. When the scene is illuminated by a single principal light source, we further include the visual clues resulting from the interaction of the geometric features of objects, the shade/shadow regions on the objects, and the “apparent contours”.  We do so by a mathematical analysis using a repertoire of methods in singularity theory. This is applied for generic light directions of both the “stable configurations” for these interactions, whose features remain unchanged under small viewer movement, and the generic changes which occur under changes of view directions. These may then be used to differentiate between objects and determine their shapes and positions.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $44.99
price for Mexico
  • ISBN 978-3-319-41471-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for Mexico
  • ISBN 978-3-319-41470-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Local Features in Natural Images via Singularity Theory
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2165
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-41471-3
DOI
10.1007/978-3-319-41471-3
Softcover ISBN
978-3-319-41470-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 255
Number of Illustrations
57 b/w illustrations, 50 illustrations in colour
Topics

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