An Invitation to 3-D Vision

From Images to Geometric Models
Sofort lieferbar | Lieferzeit: Sofort lieferbar I
997 g
241x159x38 mm
26 47, Interdisciplinary Applied Mathematics Texts in Applied Mathematics

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.
This book is intended to give undergraduate and beginning graduate students and researchers in computer vision, applied mathematics,
robotics, and computer graphics a self-contained introduction to the
geometry of 3D vision. Exercises are provided at the end of each
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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