Skip to main content
  • Textbook
  • © 1990

Group-Theoretical Methods in Image Understanding

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

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-61275-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout

This is a preview of subscription content, access via your institution.

Table of contents (10 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
    2. Introduction

      • Kenichi Kanatani
      Pages 3-20
    3. 3D Rotation and Its Irreducible Representations

      • Kenichi Kanatani
      Pages 61-102
    4. Algebraic Invariance of Image Characteristics

      • Kenichi Kanatani
      Pages 103-146
    5. Characterization of Scenes and Images

      • Kenichi Kanatani
      Pages 147-196
    6. Representation of 3D Rotations

      • Kenichi Kanatani
      Pages 197-235
  3. Principles of 3D Shape Recovery From Images

    1. Front Matter

      Pages 237-237
    2. Shape from Motion

      • Kenichi Kanatani
      Pages 239-277
    3. Shape from Angle

      • Kenichi Kanatani
      Pages 278-326
    4. Shape from Texture

      • Kenichi Kanatani
      Pages 327-355
    5. Shape from Surface

      • 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.

Keywords

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

Authors and Affiliations

  • Department of Computer Science, Gunma University Kiryu, Japan

    Kenichi Kanatani

Bibliographic Information

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-61275-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout