Group-Theoretical Methods in Image Understanding

  • Kenichi Kanatani

Part of the Springer Series in Information Sciences book series (SSINF, volume 20)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Group Theoretical Analysis of Image Characteristics

    1. Front Matter
      Pages 1-1
    2. Kenichi Kanatani
      Pages 3-20
    3. Kenichi Kanatani
      Pages 61-102
    4. Kenichi Kanatani
      Pages 103-146
    5. Kenichi Kanatani
      Pages 147-196
    6. Kenichi Kanatani
      Pages 197-235
  3. Principles of 3D Shape Recovery From Images

    1. Front Matter
      Pages 237-237
    2. Kenichi Kanatani
      Pages 239-277
    3. Kenichi Kanatani
      Pages 278-326
    4. Kenichi Kanatani
      Pages 327-355
    5. Kenichi Kanatani
      Pages 356-397
  4. Back Matter
    Pages 436-459

About this book


Image understanding is an attempt to extract knowledge about a 3D scene from 20 images. The recent development of computers has made it possible to automate a wide range of systems and operations, not only in the industry, military, and special environments (space, sea, atomic plants, etc.), but also in daily life. As we now try to build ever more intelligent systems, the need for "visual" control has been strongly recognized, and the interest in image under­ standing has grown rapidly. Already, there exists a vast body of literature-ranging from general philosophical discourses to processing techniques. Compared with other works, however, this book may be unique in that its central focus is on "mathematical" principles-Lie groups and group representation theory, in particular. In the study of the relationship between the 3D scene and the 20 image, "geometry" naturally plays a central role. Today, so many branches are inter­ woven in geometry that we cannot truly regard it as a single subject. Neverthe­ less, as Felix Klein declared in his Erlangen Program, the central principle of geometry is group theory, because geometrical concepts are abstractions of properties that are "invariant" with respect to some group of transformations. In this text, we specifically focus on two groups of transformations. One is 20 rotations of the image coordinate system around the image origin. Such coordi­ nate rotations are indeed irrelevant when we look for intrinsic image properties.


Image understanding computer vision differential geometry geometry image analysis image processing invariant machine vision solution tensor topology

Authors and affiliations

  • Kenichi Kanatani
    • 1
  1. 1.Department of Computer ScienceGunma University KiryuJapan

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-64772-7
  • Online ISBN 978-3-642-61275-6
  • Series Print ISSN 0720-678X
  • Buy this book on publisher's site