# An Invitation to 3-D Vision

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Juli 2005

## Beschreibung

### Beschreibung

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. Following a brief introduction, Part I provides background materials for the rest of the book. The two fundamental transformations, namely rigid body motion and perspective projection are introduced and image formation and feature extraction discussed. Part II covers the classic theory of two view geometry based on the so-called epipolar constraint. Part III shows that a more proper tool for studying the geometry of multiple views is the so- called rank considtion on the multiple view matrix. Part IV develops practical reconstruction algorithms step by step as well as discusses possible extensions of the theory. Exercises are provided at the end of each chapter. Software for examples and algorithms are available on the author's website.### Inhaltsverzeichnis

Preface1 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

### Pressestimmen

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)

EAN: 9780387008936

ISBN: 0387008934

Untertitel: From Images to Geometric Models.
'Interdisciplinary Applied Mathematics'.
1st ed. 2004. Corr. 2nd printing 2005.
170 Abbildungen.
Sprache: Englisch.

Verlag: Springer-Verlag GmbH

Erscheinungsdatum: Juli 2005

Seitenanzahl: XX

Format: gebunden

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