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Image Processing with Cellular Topology

  • Book
  • © 2021

Overview

Authors:
  1. Vladimir Kovalevsky

    1. Computer Science Department, University of Applied Sciences Berlin, Berlin, Germany

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  • Introduces abstract cell complex as an important tool for image processing research
  • Proposes boundary tracing and encoding methods based on abstract cell complex
  • Presents image processing as an application area to topological research community

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • Vladimir Kovalevsky
    Pages 1-6

  3. Boundary Presentation Using Abstract Cell Complexes

    • Vladimir Kovalevsky
    Pages 7-16

  4. Boundary Tracing in Binary Images Using Cell Complexes

    • Vladimir Kovalevsky
    Pages 17-27

  5. Boundary Tracing and Encoding in Color Images

    • Vladimir Kovalevsky
    Pages 29-59

  6. Boundary Polygonization

    • Vladimir Kovalevsky
    Pages 61-112

  7. Edge Detection in 2D Images

    • Vladimir Kovalevsky
    Pages 113-138

  8. Surface Traversing and Encoding in 3D Images

    • Vladimir Kovalevsky
    Pages 139-170

  9. Edge Detection in 3D Images

    • Vladimir Kovalevsky
    Pages 171-178

  10. Discussion

    • Vladimir Kovalevsky
    Pages 179-184
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Keywords

About this book

This book explains why the finite topological space known as abstract cell complex is important for successful image processing and presents image processing methods based on abstract cell complex, especially for tracing and encoding of boundaries of homogeneous regions. Many examples are provided in the book, some teach you how to trace and encode boundaries in binary, indexed and colour images. Other examples explain how to encode a boundary as a sequence of straight-line segments which is important for shape recognition. A new method of edge detection in two- and three-dimensional images is suggested. Also, a discussion problem is included in the book: A derivative is defined as the limit of the relation of the increment of the function to the increment of the argument as the latter tends to zero. Is it not better to estimate derivatives as the relation of the increment of the function to the optimal increment of the argument instead of taking exceedingly small increment whichleads to errors? This book addresses all above questions and provide the answers.


Authors and Affiliations

  • Computer Science Department, University of Applied Sciences Berlin, Berlin, Germany

    Vladimir Kovalevsky

About the author

Vladimir A. Kovalevsky received his diploma in physics from the Kharkov University (Ukraine) in 1950, the first doctoral degree in technical sciences from the Central Institute of Metrology (Leningrad) in 1957, and the second doctoral degree in computer science from the Institute of Cybernetics of the Academy of Sciences of the Ukraine (Kiev) in 1968. From 1961 to 1983 he served as Head of Department of Pattern Recognition at that Institute.

He has been living in Germany since 1983. From 1983 to 1989 he was researcher at the Central Institute of Cybernetics of the Academy of Sciences of the GDR, Berlin. From 1989 to 2004 he was professor of computer science at the University of Applied Sciences Berlin with an interruption for three years (1998-2001). In that time, he was scientific collaborator at the University of Rostock. He worked as visiting researcher at the University of Pennsylvania (1990), as visiting professor of computer sciences at the Manukau Institute of Technology, NewZealand (2005), at the Department of Automatic Control of the “Centro de Investigación y de Estudios Avanzados del IPN” in Mexico (2006), at the University of Applied Sciences Wildau, Germany (2008) and at the Chonbuk National University, Korea (2009). He has been plenary speaker at conferences in Europe, America and New Zealand. His research interests include digital geometry, digital topology, computer vision, image processing and pattern recognition. He has published four monographs and more than 180 journal and conference papers in image analysis, digital geometry and digital topology.

Bibliographic Information

  • Book Title: Image Processing with Cellular Topology

  • Authors: Vladimir Kovalevsky

  • DOI: https://doi.org/10.1007/978-981-16-5772-6

  • Publisher: Springer Singapore

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021

  • Hardcover ISBN: 978-981-16-5771-9Published: 29 March 2022

  • Softcover ISBN: 978-981-16-5774-0Published: 30 March 2023

  • eBook ISBN: 978-981-16-5772-6Published: 26 March 2022

  • Edition Number: 1

  • Number of Pages: XI, 184

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Computer Imaging, Vision, Pattern Recognition and Graphics, Signal, Image and Speech Processing, Topology

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