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  • © 2004

An Invitation to 3-D Vision

From Images to Geometric Models

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Part of the book series: Interdisciplinary Applied Mathematics (IAM, volume 26)

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  • ISBN: 978-0-387-21779-6
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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xx
  2. Introduction

    1. Introduction

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 1-12
  3. Introductory Material

    1. Front Matter

      Pages 13-13
    2. Representation of a Three-Dimensional Moving Scene

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 15-43
    3. Image Formation

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 44-74
    4. Image Primitives and Correspondence

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 75-106
  4. Geometry of Two Views

    1. Front Matter

      Pages 107-107
    2. Reconstruction from Two Calibrated Views

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 109-170
    3. Reconstruction from Two Uncalibrated Views

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 171-227
    4. Estimation of Multiple Motions from Two Views

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 228-260
  5. Geometry of Multiple Views

    1. Front Matter

      Pages 261-261
    2. Multiple-View Geometry of Points and Lines

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 263-309
    3. Extension to General Incidence Relations

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 310-337
    4. Geometry and Reconstruction from Symmetry

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 338-372
  6. Applications

    1. Front Matter

      Pages 373-373
    2. Step-by-Step Building of a 3-D Model from Images

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 375-411
    3. Visual Feedback

      • Yi Ma, Stefano Soatto, Jana Košecká, S. Shankar Sastry
      Pages 412-438
  7. Back Matter

    Pages 439-527

About this book

Endowing machines with a sense of vision has been a dream of scientists and engineers alike for over half a century. Only in the past decade, however, has the geometry of vision been understood to the point where this dream becomes attainable, thanks also to the remarkable progress in imaging and computing hardware.

This book addresses a central problem in computer vision -- how to recover 3-D structure and motion from a collection of 2-D images -- using techniques drawn mainly from linear algebra and matrix theory. The stress is on developing a unified framework for studying the geometry of multiple images of a 3-D scene and reconstructing geometric models from those images. The book also covers relevant aspects of image formation, basic image processing, and feature extraction. The authors bridge the gap between theory and practice by providing step-by-step instructions for the implementation of working vision algorithms and systems.

Written primarily as a textbook, the aim of this book is to give senior undergraduate and beginning graduate students in computer vision, robotics, and computer graphics a solid theoretical and algorithmic foundation for future research in this burgeoning field. It is entirely self-contained with necessary background material covered in the beginning chapters and appendices, and plenty of exercises, examples, and illustrations given throughout the text.

Keywords

  • 3D
  • Tracking
  • algorithms
  • computer graphics
  • computer vision
  • filtering
  • linear algebra
  • linear optimization
  • nonlinear optimization
  • optimization
  • robot
  • robotics

Reviews

From the reviews:

"Computer vision is invading our daily lives … . Covering all the aspects would be too vast an area to cover in one book, so here, the authors concentrated on the specific goal of recovering the geometry of a 3D object … . The 22 pages of references form a good guide to the literature. The authors found an excellent balance between a thorough mathematical treatment and the applications themselves. … the text will be a pleasure to read for students … ." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 12 (2), 2005)

"This is primarily a textbook of core principles, taking the reader from the most basic concepts of machine vision … to detailed applications, such as autonomous vehicle navigation. … It is a clearly written book … . Everything that is required is introduced … . an entirely self-contained work. … The book is aimed at graduate or advanced undergraduate students in electrical engineering, computer science, applied mathematics, or indeed anyone interested in machine vision … . is highly recommended." (D.E. Holmgren, The Photogrammetric Record, 2004)

"This very interesting book is a great book teaching how to go from two-dimensional (2D)-images to three-dimensional (3D)-models of the geometry of a scene. … A good part of this book develops the foundations of an appropriate mathematical approach necessary for solving those difficult problems. … Exercises (drill exercises, advanced exercises and programming exercises) are provided at the end of each chapter." (Hans-Dietrich Hecker, Zentralblatt MATH, Vol. 1043 (18), 2004)

"This book gives senior undergraduate and beginning graduate students and researchers in computer vision, applied mathematics, computer graphics, and robotics a self-contained introduction to the geometry of 3D vision. That is the reconstruction of 3D models of objects from a collection of 2D images. … Exercises are provided at the end of each chapter. Software for examples and algorithms are available on the author’s website." (Daniel Leitner, Simulation News Europe, Vol. 16 (1), 2006)

Authors and Affiliations

  • Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, USA

    Yi Ma

  • Department of Computer Science, University of California, Los Angeles, Los Angeles, USA

    Stefano Soatto

  • Department of Computer Science, George Mason University, Fairfax, USA

    Jana Košecká

  • Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, USA

    S. Shankar Sastry

Bibliographic Information

Buying options

eBook
USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-0-387-21779-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 79.99
Price excludes VAT (USA)
Hardcover Book
USD 119.99
Price excludes VAT (USA)