An Invitation to 3-D Vision
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An Invitation to 3-D Vision : From Images to Geometric Models

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Description

This book introduces the geometry of 3-D vision, that is, the reconstruction of 3-D models of objects from a collection of 2-D images. It details the classic theory of two view geometry and shows that a more proper tool for studying the geometry of multiple views is the so-called rank consideration of the multiple view matrix. It also develops practical reconstruction algorithms and discusses possible extensions of the theory.
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Product details

  • Hardback | 528 pages
  • 155 x 235 x 30.23mm | 2,090g
  • New York, NY, United States
  • English
  • 1st ed. 2004. Corr. 2nd printing 2005
  • XX, 528 p.
  • 0387008934
  • 9780387008936
  • 1,152,460

Back cover copy

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.
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Table of contents

Preface
1 Introduction
1.1 Visual perception: from 2-D images to 3-D models
1.2 A mathematical approach
1.3 A historical perspective
I Introductory material
2 Representation of a three-dimensional moving scene
2.1 Three-dimensional Euclidean space
2.2 Rigid body motion
2.3 Rotational motion and its representations
2.4 Rigid body motion and its representations
2.5 Coordinate and velocity transformations
2.6 Summary
2.7 Exercises
2.A Quaternions and Euler angles for rotations
3 Image formation
3.1 Representation of images
3.2 Lenses, light, and basic photometry
3.3 A geometric model of image formation
3.4 Summary
3.5 Exercises
3.A Basic photometry with light sources and surfaces
3.B Image formation in the language of projective geometry
4 Image primitives and correspondence
4.1 Correspondence of geometric features
4.2 Local deformation models
4.3 Matching point features
4.4 Tracking line features
4.5 Summary
4.6 Exercises
4.A Computing image gradients
II Geometry of two views
5 Reconstruction from two calibrated views
5.1 Epipolar geometry
5.2 Basic reconstruction algorithms
5.3 Planar scenes and homography
5.4 Continuous motion case
5.5 Summary
5.6 Exercises
5.A Optimization subject to epipolar constraint
6 Reconstruction from two uncalibrated views
6.1 Uncalibrated camera or distorted space?
6.2 Uncalibrated epipolar geometry
6.3 Ambiguities and constraints in image formation
6.4 Stratified reconstruction
6.5 Calibration with scene knowledge
6.6 Dinner with Kruppa
6.7 Summary
6.8 Exercises
6.A From images to Fundamental matrices
6.B Properties of Kruppa's equations
7 Segmentation of multiple moving objects from two views
7.1 Multibody epipolar constraint and Fundamental matrix
7.2 A rank condition for the number of motions
7.3 Geometric properties of the multibody Fundamental matrix
7.4 Multibody motion estimation and segmentation
7.5 Multibody structure from motion
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Review Text

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)
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Review quote

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)
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Rating details

13 ratings
4.15 out of 5 stars
5 46% (6)
4 31% (4)
3 15% (2)
2 8% (1)
1 0% (0)
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