Computer Vision: Three-dimensional Reconstruction Techniques

Foreword
Preface
Acknowledgements
Contents
Acronyms
Listings
1 Introduction
	1.1 The Prodigy of Vision
	1.2 Low-Level Computer Vision
	1.3 Overview of the Book
	1.4 Notation
	References
2 Fundamentals of Imaging
	2.1 Introduction
	2.2 Perspective
	2.3 Digital Images
	2.4 Thin Lenses
		2.4.1 Telecentric Optics
	2.5 Radiometry
	References
3 The Pinhole Camera Model
	3.1 Introduction
	3.2 Pinhole Camera
	3.3 Simplified Pinhole Model
	3.4 General Pinhole Model
		3.4.1 Intrinsic Parameters
			3.4.1.1 Field of View
		3.4.2 Extrinsic Parameters
	3.5 Dissection of the Perspective Projection Matrix
		3.5.1 Collinearity Equations
	3.6 Radial Distortion
	Problems
	References
4 Camera Calibration
	4.1 Introduction
	4.2 The Direct Linear Transform Method
	4.3 Factorisation of the Perspective Projection Matrix
	4.4 Calibrating Radial Distortion
	4.5 The Sturm-Maybank-Zhang Calibration Algorithm
	Problems
	References
5 Absolute and Exterior Orientation
	5.1 Introduction
	5.2 Absolute Orientation
		5.2.1 Orthogonal Procrustes Analysis
	5.3 Exterior Orientation
		5.3.1 Fiore's Algorithm
		5.3.2 Procrustean Method
		5.3.3 Direct Method
	Problems
	References
6 Two-View Geometry
	6.1 Introduction
	6.2 Epipolar Geometry
	6.3 Fundamental Matrix
	6.4 Computing the Fundamental Matrix
		6.4.1 The Seven-Point Algorithm
		6.4.2 Preconditioning
	6.5 Planar Homography
		6.5.1 Computing the Homography
	6.6 Planar Parallax
	Problems
	References
7 Relative Orientation
	7.1 Introduction
	7.2 The Essential Matrix
		7.2.1 Geometric Interpretation
		7.2.2 Computing the Essential Matrix
	7.3 Relative Orientation from the Essential Matrix
		7.3.1 Closed Form Factorisation of the Essential Matrix
	7.4 Relative Orientation from the Calibrated Homography
	Problems
	References
8 Reconstruction from Two Images
	8.1 Introduction
	8.2 Triangulation
	8.3 Ambiguity of Reconstruction
	8.4 Euclidean Reconstruction
	8.5 Projective Reconstruction
	8.6 Euclidean Upgrade from Known Intrinsic Parameters
	8.7 Stratification
	Problems
	References
9 Non-linear Regression
	9.1 Introduction
	9.2 Algebraic Versus Geometric Distance
	9.3 Non-linear Regression of the PPM
		9.3.1 Residual
		9.3.2 Parameterisation
		9.3.3 Derivatives
		9.3.4 General Remarks
	9.4 Non-linear Regression of Exterior Orientation
	9.5 Non-linear Regression of a Point in Space
		9.5.1 Residual
		9.5.2 Derivatives
		9.5.3 Radial Distortion
	9.6 Regression in the Joint Image Space
	9.7 Non-linear Regression of the Homography
		9.7.1 Residual
		9.7.2 Parameterisation
		9.7.3 Derivatives
	9.8 Non-linear Regression of the Fundamental Matrix
		9.8.1 Residual
		9.8.2 Parameterisation
		9.8.3 Derivatives
	9.9 Non-linear Regression of Relative Orientation
		9.9.1 Parameterisation
		9.9.2 Derivatives
	9.10 Robust Regression
	Problems
	References
10 Stereopsis: Geometry
	10.1 Introduction
	10.2 Triangulation in the Normal Case
	10.3 Epipolar Rectification
		10.3.1 Calibrated Rectification
		10.3.2 Uncalibrated Rectification
	Problems
	References
11 Features Points
	11.1 Introduction
	11.2 Filtering Images
		11.2.1 Smoothing
			11.2.1.1 Non-linear Filters
		11.2.2 Derivation
	11.3 LoG Filtering
	11.4 Harris-Stephens Operator
		11.4.1 Matching and Tracking
		11.4.2 Kanade-Lucas-Tomasi Algorithm
		11.4.3 Predictive Tracking
	11.5 Scale Invariant Feature Transform
		11.5.1 Scale-Space
		11.5.2 SIFT Detector
		11.5.3 SIFT Descriptor
		11.5.4 Matching
	References
12 Stereopsis: Matching
	12.1 Introduction
	12.2 Constraints and Ambiguities
	12.3 Local Methods
		12.3.1 Matching Cost
		12.3.2 Census Transform
	12.4 Adaptive Support
		12.4.1 Multiresolution Stereo Matching
		12.4.2 Adaptive Windows
	12.5 Global Matching
	12.6 Post-Processing
		12.6.1 Reliability Indicators
		12.6.2 Occlusion Detection
	References
13 Range Sensors
	13.1 Introduction
	13.2 Structured Lighting
		13.2.1 Active Stereopsis
		13.2.2 Active Triangulation
		13.2.3 Ray-Plane Triangulation
		13.2.4 Scanning Methods
		13.2.5 Coded-Light Methods
	13.3 Time-of-Flight Sensors
	13.4 Photometric Stereo
		13.4.1 From Normals to Coordinates
	13.5 Practical Considerations
	References
14 Multi-View Euclidean Reconstruction
	14.1 Introduction
		14.1.1 Epipolar Graph
		14.1.2 The Case of Three Images
		14.1.3 Taxonomy
	14.2 Point-Based Approaches
		14.2.1 Adjustment of Independent Models
		14.2.2 Incremental Reconstruction
		14.2.3 Hierarchical Reconstruction
	14.3 Frame-Based Approach
		14.3.1 Synchronisation of Rotations
		14.3.2 Synchronisation of Translations
		14.3.3 Localisation from Bearings
	14.4 Bundle Adjustment
		14.4.1 Jacobian of Bundle Adjustment
		14.4.2 Reduced System
	References
15 3D Registration
	15.1 Introduction
		15.1.1 Generalised Procrustes Analysis
	15.2 Correspondence-Less Methods
		15.2.1 Registration of Two Point Clouds
		15.2.2 Iterative Closest Point
		15.2.3 Registration of Many Point Clouds
	References
16 Multi-view Projective Reconstruction and Autocalibration
	16.1 Introduction
		16.1.1 Sturm-Triggs Factorisation Method
	16.2 Autocalibration
		16.2.1 Absolute Quadric Constraint
			16.2.1.1 Solution Strategies
		16.2.2 Mendonça-Cipolla Method
	16.3 Autocalibration via H∞
	16.4 Tomasi-Kanade's Factorisation
		16.4.1 Affine Camera
		16.4.2 The Factorisation Method for Affine Camera
	Problems
	References
17 Multi-view Stereo Reconstruction
	17.1 Introduction
	17.2 Volumetric Stereo in Object-Space
		17.2.1 Shape from Silhouette
		17.2.2 Szeliski's Algorithm
		17.2.3 Voxel Colouring
		17.2.4 Space Carving
	17.3 Volumetric Stereo in Image-Space
	17.4 Marching Cubes
	References
18 Image-Based Rendering
	18.1 Introduction
	18.2 Parametric Transformations
		18.2.1 Mosaics
			18.2.1.1 Alignment
			18.2.1.2 Blending
		18.2.2 Image Stabilisation
		18.2.3 Perspective Rectification
	18.3 Non-parametric Transformations
		18.3.1 Transfer with Depth
		18.3.2 Transfer with Disparity
		18.3.3 Epipolar Transfer
		18.3.4 Transfer with Parallax
		18.3.5 Ortho-Projection
	18.4 Geometric Image Transformation
	Problems
	References
A Notions of Linear Algebra
	A.1 Introduction
	A.2 Scalar Product
	A.3 Matrix Norm
	A.4 Inverse Matrix
	A.5 Determinant
	A.6 Orthogonal Matrices
	A.7 Linear and Quadratic Forms
	A.8 Rank
	A.9 QR Decomposition
	A.10 Eigenvalues and Eigenvectors
	A.11 Singular Value Decomposition
	A.12 Pseudoinverse
	A.13 Cross Product
	A.14 Kronecker's Product
	A.15 Rotations
	A.16 Matrices Associated with Graphs
	References
B Matrix Differential Calculation
	B.1 Derivatives of Vector and Matrix Functions
	B.2 Derivative of Rotations
		B.2.1 Axis/Angle Representation
		B.2.2 Euler Representation
	References
C Regression
	C.1 Introduction
	C.2 Least-Squares
		C.2.1 Linear Least-Squares
		C.2.2 Non-linear Least-Squares
			C.2.2.1 Gauss-Newton Method
		C.2.3 The Levenberg-Marquardt Method
	C.3 Robust Regression
		C.3.1 Outliers and Robustness
		C.3.2 M-Estimators
		C.3.3 Least Median of Squares
		C.3.4 RANSAC
	C.4 Propagation of Uncertainty
		C.4.1 Covariance Propagation in Least-Squares
	References
D Notions of Projective Geometry
	D.1 Introduction
	D.2 Perspective Projection
	D.3 Homogeneous Coordinates
	D.4 Equation of the Line
	D.5 Transformations
	Reference
E Matlab Code
Index