Authors:
- Offers a clear introduction to the computational topology of digital images
- Focuses on the application of computational topology in the shape analysis of visual scenes
- Presents applications of computation topology in a variety of visual contexts and sample solutions to problems with Mathematica and Matlab
Part of the book series: Intelligent Systems Reference Library (ISRL, volume 162)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structures that infuse triangulated visual scenes.
The book first addresses the topology of cellular complexes to provide a basis for an introductory study of the computational topology of visual scenes, exploring the fabric, shapes and structures typically found in visual scenes. The book then examines the inherent geometry and topology of visual scenes, and the fine structure of light and light caustics of visual scenes, which bring into play catastrophe theory and the appearance of light caustic folds and cusps. Following on from this, the book introduces optical vortex nerves in triangulated digital images. In this context, computationalphysics is synonymous with the study of the fine structure of light choreographed in video frames. This choreography appears as a sequence of snapshots of light reflected and refracted from surface shapes, providing a solid foundation for detecting, analyzing and classifying visual scene shapes.
Reviews
“The book is presented in a very accessible fashion. … The book is suitable for graduate students and researchers interested in computational geometry and computer vision. Moreover, it can be used as a professional reference.” (Krzysztof Gdawiec, zbMATH 1437.68005, 2020)
Authors and Affiliations
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Department of Electrical and Computer Engineering, Engineering and Information Technology Complex, University of Manitoba, Winnipeg, Canada
James F. Peters
Bibliographic Information
Book Title: Computational Geometry, Topology and Physics of Digital Images with Applications
Book Subtitle: Shape Complexes, Optical Vortex Nerves and Proximities
Authors: James F. Peters
Series Title: Intelligent Systems Reference Library
DOI: https://doi.org/10.1007/978-3-030-22192-8
Publisher: Springer Cham
eBook Packages: Intelligent Technologies and Robotics, Intelligent Technologies and Robotics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-22191-1Published: 15 October 2019
Softcover ISBN: 978-3-030-22194-2Published: 15 October 2020
eBook ISBN: 978-3-030-22192-8Published: 03 October 2019
Series ISSN: 1868-4394
Series E-ISSN: 1868-4408
Edition Number: 1
Number of Pages: XXV, 440
Number of Illustrations: 1648 b/w illustrations, 205 illustrations in colour
Topics: Computational Intelligence, Artificial Intelligence, Image Processing and Computer Vision, Signal, Image and Speech Processing