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计算机视觉_一种现代方法.英文版.pdf
CONTENTS
PREFACE
Part I IMAGE FORMATION
Chapter 1 CAMERAS
1.1 Pinhole Cameras
1.1.1 Perspective Projection
1.1.2 Affine Projection
1.1.3 Spherical Projection
1.2 Cameras with Lenses
1.2.1 First-Order Geometric Optics
1.2.2 Thin Lenses: Geometry
1.2.3 Thin Lenses: Radiometry
1.2.4 Real Lenses
1.3 Sensing
1.3.1 CCD cameras
1.3.2 Sensor Models
1.4 Notes
1.5 Assignments
Chapter 2 RADIOMETRY -MEASURING LIGHT
2.1 Light in Space
2.1.1 Foreshortening
2.1.2 Solid Angle
2.1.3 Radiance
2.2 Light at Surfaces
2.2.1 Simplifying Assumptions
2.2.2 The Bidirectional Reflectance Distribution Function
2.3 Important Special Cases
2.3.1 Radiosity
2.3.2 Directional Hemispheric Reflectance
2.3.3 Lambertian Surfaces and Albedo
2.3.4 Specular Surfaces
2.3.5 The Lambertian + Specular Model
2.4 Quick Reference: Radiometric Terminology for Light
2.5 Quick Reference: Radiometric Properties of Surfaces
2.6 Quick Reference: Important Types of Surface
2.7 Comments
2.8 Assignments
Chapter 3 SOURCES, SHADOWS AND SHADING
3.1 Radiometric Properties of Light Sources
3.2 Qualitative Radiometry
3.3 Sources and their Effects
3.3.1 Point Sources
3.3.2 Line Sources
3.3.3 Area Sources
3.4 Local Shading Models
3.4.1 Local Shading Models for Point Sources
3.4.2 Area Sources and their Shadows
3.4.3 Ambient Illumination
3.5 Application: Photometric Stereo
3.5.1 Normal and Albedo from Many Views
3.5.2 Shape from Normals
3.6 Interreflections: Global Shading Models
3.6.1 An Interreflection Model
3.6.2 Solving for Radiosity
3.6.3 The qualitative effects of interreflections
3.7 Notes
3.7.1 Local Shading Models
3.7.2 Interreflections
3.7.3 Photometric Stereo
3.7.4 Alternative Shading Representations
3.8 Assignments
3.8.1 Exercises
3.8.2 Programming Assignments
Chapter 4 COLOUR
4.1 The Physics of Colour
4.1.1 Radiometry for Coloured Lights: Spectral Quantities
4.1.2 The Colour of Surfaces
4.1.3 The Colour of Sources
4.2 Human Colour Perception
4.2.1 Colour Matching
4.2.2 Colour Receptors
4.3 Representing Colour
4.3.1 Linear Colour Spaces
4.3.2 Non-linear Colour Spaces
4.3.3 Spatial and Temporal Effects
4.4 A Model for Image Colour
4.4.1 Cameras
4.4.2 A Model for Image Colour
4.4.3 Application: Finding Specularities
4.5 Surface Colour from Image Colour
4.5.1 Surface Colour Perception in People
4.5.2 Inferring Lightness
4.5.3 Surface Colour from Finite Dimensional Linear Models
4.6 Notes
4.6.1 Trichromacy and Colour Spaces
4.6.2 Specularity Finding
4.6.3 Lightness
4.6.4 Colour Constancy
4.6.5 Colour in Recognition
4.7 Assignments
Part II IMAGE MODELS
Chapter 5 GEOMETRIC CAMERA MODELS
5.1 Elements of Analytical Euclidean Geometry
5.1.1 Coordinate Systems and Homogeneous Coordinates
5.1.2 Coordinate System Changes and Rigid Transformations
5.2 Geometric Camera Parameters
5.2.1 Intrinsic Parameters
5.2.2 Extrinsic Parameters
5.2.3 A Characterization of Perspective Projection Matrices
5.3 Straight Lines and their Projections
5.3.1 Elements of Line Geometry
5.3.2 Projection Equations
5.4 Notes
5.5 Assignments
Chapter 6 GEOMETRIC CAMERA CALIBRATION
6.1 Least-Squares Parameter Estimation
6.1.1 Linear Least-Squares Methods
6.1.2 Non-Linear Least-Squares Methods
6.2 A Linear Approach to Camera Calibration
6.2.1 Estimation of the Projection Matrix
6.2.2 Estimation of the Intrinsic and Extrinsic Parameters
6.2.3 Degenerate Point Configurations
6.3 Taking Radial Distortion into Account
6.3.1 Estimation of the Projection Matrix
6.3.2 Estimation of the Intrinsic and Extrinsic Parameters
6.3.3 Degenerate Point Configurations
6.4 Using Straight Lines for Calibration
6.5 Analytical Photogrammetry
6.6 An Application: Mobile Robot Localization
6.7 Notes
6.8 Assignments
Chapter 7 AN INTRODUCTION TO PROBABILITY
7.1 Probability in Discrete Spaces
7.1.1 Probability: the P-function
7.1.2 Conditional Probability
7.1.3 Choosing P
7.2 Probability in Continuous Spaces
7.2.1 Event Structures for Continuous Spaces
7.2.2 Representing P-functions
7.2.3 Representing P-functions with Probability Density Functions
7.3 Random Variables
7.3.1 Conditional Probability and Independence
7.3.2 Expectations
7.3.3 Joint Distributions and Marginalization
7.4 Standard Distributions and Densities
7.4.1 The Normal Distribution
7.5 Probabilistic Inference
7.5.1 The Maximum Likelihood Principle
7.5.2 Priors, Posteriors and Bayes’ rule
7.5.3 Bayesian Inference
7.5.4 Open Issues
7.6 Discussion
Chapter 8 LINEAR FILTERS
8.1 Linear Filters and Convolution
8.1.1 Convolution
8.2 Shift invariant linear systems
8.2.1 Discrete Convolution
8.2.2 Continuous Convolution
8.2.3 Edge Effects in Discrete Convolutions
8.3 Spatial Frequency and Fourier Transforms
8.3.1 Fourier Transforms
8.4 Sampling and Aliasing
8.4.1 Sampling
8.4.2 Aliasing
8.4.3 Smoothing and Resampling
8.5 Technique: Scale and Image Pyramids
8.5.1 The Gaussian Pyramid
8.5.2 Applications of Scaled Representations
8.5.3 Scale Space
8.6 Discussion
8.6.1 Real Imaging Systems vs Shift-Invariant Linear Systems
8.6.2 Scale
8.6.3 Anisotropic Scaling
Chapter 9 EDGE DETECTION
9.1 Noise
9.1.1 Additive Stationary Gaussian Noise
9.1.2 Why Finite Differences Respond to Noise
9.2 Estimating Derivatives
9.2.1 Choosing a Smoothing Filter
9.2.2 Why Smooth with a Gaussian?
9.2.3 Derivative of Gaussian Filters
9.3 Detecting Edges
9.3.1 Using the Laplacian to Detect Edges
9.3.2 Gradient Based Edge Detectors
9.3.3 Technique: Orientation Representations and Corners
9.4 Commentary
Chapter 10 FILTERS AND FEATURES
10.1 Filters as Templates
10.1.1 Convolution as a Dot Product
10.1.2 Changing Basis
10.2 Technique: Normalised Correlation and Finding Patterns
10.2.1 Controlling the Television by Finding Hands by NormalisedCorrelation
10.3 Human Vision: Filters and Primate Early Vision
10.3.1 The Visual Pathway
10.3.2 The Response of Retinal Cells
10.3.3 The Lateral Geniculate Nucleus
10.3.4 The Visual Cortex
10.3.5 A Model of Early Spatial Vision
10.4 Advanced Smoothing Strategies and Non-linear Filters
10.4.1 More Noise Models
10.4.2 Robust Estimates
10.4.3 Median Filters
10.4.4 Mathematical morphology: erosion and dilation
10.5 Commentary
Chapter 11 TEXTURE
11.1 Representing Texture
11.1.1 Extracting Image Structure with Filter Banks
11.2 Analysis (and Synthesis) Using Oriented Pyramids
11.2.1 The Laplacian Pyramid
11.2.2 Filters in the Spatial Frequency Domain
11.2.3 Oriented Pyramids
11.3 Application: Synthesizing Textures for Rendering
11.3.1 Homogeneity
11.3.2 Synthesis by Matching Histograms of Filter Responses
11.3.3 Synthesis by Sampling Conditional Densities of Filter Responses
11.3.4 Synthesis by Sampling Local Models
11.4 Shape from Texture
11.4.1 Shape from Texture for Planes
11.4.2 Shape from Texture for Curved Surfaces
11.5 Notes
11.5.1 Filters, Pyramids and Efficiency
11.5.2 Texture Synthesis
11.5.3 Shape from Texture
Part IV EARLY VISION: MULTIPLE IMAGES
Chapter 12 THE GEOMETRY OF MULTIPLE VIEWS
12.1 Two Views
12.1.1 Epipolar Geometry
12.1.2 The Calibrated Case
12.1.3 Small Motions
12.1.4 The Uncalibrated Case
12.1.5 Weak Calibration
12.2 Three Views
12.2.1 Trifocal Geometry
12.2.2 The Calibrated Case
12.2.3 The Uncalibrated Case
12.2.4 Estimation of the Trifocal Tensor
12.3 More Views
12.4 Notes
12.5 Assignments
Chapter 13 STEREOPSIS
13.1 Reconstruction
13.1.1 Camera Calibration
13.1.2 Image Rectification
Human Vision: Stereopsis
13.2 Binocular Fusion
13.2.1 Correlation
13.2.2 Multi-Scale Edge Matching
13.2.3 Dynamic Programming
13.3 Using More Cameras
13.3.1 Trinocular Stereo
13.3.2 Multiple-Baseline Stereo
13.4 Notes
13.5 Assignments
Chapter 14 AFFINE STRUCTURE FROM MOTION
14.1 Elements of Affine Geometry
14.2 Affine Structure from Two Images
14.2.1 The Affine Structure-from-Motion Theorem
14.2.2 Rigidity and Metric Constraints
14.3 Affine Structure from Multiple Images
14.3.1 The Affine Structure of Affine Image Sequences
14.3.2 A Factorization Approach to Affine Motion Analysis
14.4 From Affine to Euclidean Images
14.4.1 Euclidean Projection Models
14.4.2 From Affine to Euclidean Motion
14.5 Affine Motion Segmentation
14.5.1 The Reduced Echelon Form of the Data Matrix
14.5.2 The Shape Interaction Matrix
14.6 Notes
14.7 Assignments
Chapter 15 PROJECTIVE STRUCTURE FROM MOTION
15.1 Elements of Projective Geometry
15.1.1 Projective Bases and Projective Coordinates
15.1.2 Projective Transformations
15.1.3 Affine and Projective Spaces
15.1.4 Hyperplanes and Duality
15.1.5 Cross-Ratios
15.1.6 Application: Parameterizing the Fundamental Matrix
15.2 Projective Scene Reconstruction from Two Views
15.2.1 Analytical Scene Reconstruction
15.2.2 Geometric Scene Reconstruction
15.3 Motion Estimation from Two or Three Views
15.3.1 Motion Estimation from Fundamental Matrices
15.3.2 Motion Estimation from Trifocal Tensors
15.4 Motion Estimation from Multiple Views
15.4.1 A Factorization Approach to Projective Motion Analysis
15.4.2 Bundle Adjustment
15.5 From Projective to Euclidean Structure and Motion
15.5.1 Metric Upgrades from (Partial) Camera Calibration
15.5.2 Metric Upgrades from Minimal Assumptions
15.6 Notes
15.7 Assignments
Part V MID-LEVEL VISION
Chapter 16 SEGMENTATION BY CLUSTERING
16.1 What is Segmentation?
16.1.1 Four Model Problems
16.1.2 Segmentation as Clustering
16.2 Human vision: Grouping and Gestalt
16.3 Applications: Shot Boundary Detection and BackgroundSubtraction
16.3.1 Background Subtraction
16.3.2 Shot Boundary Detection
16.4 Image Segmentation by Clustering Pixels
16.4.1 Segmentation Using Simple Clustering Methods
16.4.2 Clustering and Segmentation by K-means
16.5 Segmentation by Graph-Theoretic Clustering
16.5.1 Terminology for Graphs
16.5.2 The Overall Approach
16.5.3 Affinity Measures
16.5.4 Eigenvectors and Segmentation
16.5.5 Normalised Cuts
16.6 Discussion
16.6.1 Segmentation and Grouping in People
16.6.2 Perceptual Grouping
Chapter 17 SEGMENTATION BY FITTING A MODEL
17.1 Fitting Lines
17.1.1 The Hough Transform
17.1.2 Line Fitting with Least Squares
17.1.3 Which Point is on Which Line?
17.2 Fitting Curves
17.2.1 Implicit Curves
17.2.2 Parametric Curves
17.3 Example: Finding Body Segments by Fitting
17.3.1 Some Relations Between Surfaces and Outlines
17.3.2 Using Constraints to Fit SOR Outlines
17.4 Fitting as a Probabilistic Inference Problem
17.5 Robustness
17.5.1 M-estimators
17.5.2 RANSAC
17.6 Example: Using RANSAC to Fit Fundamental Matrices
17.6.1 An Expression for Fitting Error
17.6.2 Correspondence as Noise
17.6.3 Applying RANSAC
17.7 Discussion
Chapter 18 SEGMENTATION AND FITTING USING PROBABILISTIC METH-ODS5
18.1 Missing Data Problems, Fitting and Segmentation
18.1.1 Missing Data Problems
18.1.2 The EM Algorithm
18.1.3 The EM Algorithm in the General Case
18.2 The EM Algorithm in Practice
18.2.1 Example: Image Segmentation, Revisited
18.2.2 Example: Line Fitting with EM
18.2.3 Example: Motion Segmentation and EM
18.2.4 Example: Using EM to Identify Outliers
18.2.5 Example: Background Subtraction using EM
18.2.6 Example: Finding Body Segments with EM
18.2.7 Example: EM and the Fundamental Matrix
18.2.8 Difficulties with the EM Algorithm
18.3 How Many are There?
18.3.1 Basic Ideas
18.3.2 AIC — An Information Criterion
18.3.3 Bayesian methods and Schwartz’ BIC
18.3.4 Description Length
18.3.5 Other Methods for Estimating Deviance
18.4 Discussion
18.4.1 EM and Missing Variable Models
18.4.2 Model Selection
Chapter 19 TRACKING WITH LINEAR DYNAMIC MODELS
19.1 Tracking as an Abstract Inference Problem
19.1.1 Independence Assumptions
19.1.2 Tracking as Inference
19.1.3 Overview
19.2 Linear Dynamic Models
19.2.1 Drifting Point
19.2.2 Constant Velocity
19.2.3 Constant Acceleration
19.2.4 Periodic Motion
19.2.5 Higher Order Models
19.3 Kalman Filtering
19.3.1 The Kalman Filter for a 1D State Vector
19.3.2 The Kalman Update Equations for a General State Vector
19.3.3 Forward-Backward Smoothin
19.4 Applications and Examples
19.4.1 Vehicle Tracking
19.5 Discussion
Chapter 20 TRACKING WITH NON-LINEAR DYNAMIC MODELS
20.1 Non-Linear Dynamic Models
20.1.1 Unpleasant Properties of Non-Linear Dynamics
20.1.2 Difficulties with Likelihoods
20.2 Particle Filtering
20.2.1 Sampled Representations of Probability Distribut
20.2.2 The Simplest Particle Filter
20.2.3 A Workable Particle Filter
20.2.4 If’s, And’s and But’s — Practical Issues in Building ParticleFilters
20.3 Tracking People with Particle Filters
20.4 Data Association
20.4.1 Choosing the Nearest — Global Nearest Neighbours
20.4.2 Gating and Probabilistic Data Association
20.5 Discussion
20.5.1 The Particle Filter
20.5.2 Starting a People Tracker
II Appendix: The Extended Kalman Filter, or EKF
Part VI APPLICATIONS AND TOPICS
Chapter 21 RANGE DATA
21.1 Active Range Sensors
21.2 Range Data Segmentation
21.2.1 Finding Step and Roof Edges in Range Images
21.2.2 Segmenting Range Images into Planar Regions
21.3 Range Image Registration and Model Construction
21.3.1 Registering Range Images Using the Iterative Closest-Point Method
21.3.2 Fusing Multiple Range Images
21.4 Object Recognition
21.4.1 Matching Piecewise-Planar Surfaces Using InterpretationTrees
21.4.2 Matching Free-Form Surfaces Using Spin Images
21.5 Notes
21.6 Assignments
Chapter 22 APPLICATION: FINDING IN DIGITAL LIBRARIES
22.1 Background: Organizing Collections of Information
22.1.1 How Well does the System Work?
22.1.2 What do Users want?
22.1.3 Searching for Pictures
22.1.4 Structuring and Browsing
22.2 Summary Representations of the Whole Picture
22.2.1 Histograms and Correlograms
22.2.2 Textures and Textures of Textures
22.3 Representations of Parts of the Picture
22.3.1 Segmentation
22.3.2 Template matching
22.3.3 Shape and correspondence
22.3.4 Clustering and Organising Collections
22.4 Video
22.5 Discussion
Chapter 23 APPLICATION:IMAGE-BASED RENDERING
23.1 Constructing 3D Models from Image Sequences
23.1.1 Scene Modeling from Registered Images
23.1.2 Scene Modeling from Unregistered Images
23.2 Transfer-Based Approaches to Image-Based Rendering
23.2.1 Affine View Synthesis
23.2.2 Euclidean View Synthesis
23.3 The Light Field
23.4 Notes
23.5 Assignments
Part VII HIGH-LEVEL VISION
Chapter 24 CORRESPONDENCE AND POSE CONSISTENCY
24.1 Initial Assumptions
24.1.1 Obtaining Hypotheses
24.2 Obtaining Hypotheses by Pose Consistency
24.2.1 Pose Consistency for Perspective Cameras
24.2.2 Affine and Projective Camera Models
24.2.3 Linear Combinations of Models
24.3 Obtaining Hypotheses by Pose Clustering
24.4 Obtaining Hypotheses Using Invariants
24.4.1 Invariants for Plane Figures
24.4.2 Geometric Hashing
24.4.3 Invariants and Indexing
24.5 Verification
24.5.1 Edge Proximity
24.5.2 Similarity in Texture, Pattern and Intensity
24.5.3 Example: Bayes Factors and Verification
24.6 Application: Registration in Medical Imaging Systems
24.6.1 Imaging Modes
24.6.2 Applications of Registration
24.6.3 Geometric Hashing Techniques in Medical Imaging
24.7 Curved Surfaces and Alignment
24.8 Discussion
24.8.1 Medical applications
Chapter 25 FINDING TEMPLATES USING CLASSIFIERS
25.1 Classifiers
25.1.1 Using Loss to Determine Decisions
25.1.2 Overview: Methods for Building Classifiers
25.1.3 Example: A Plug-in Classifier for Normal Class-conditionalDensities
25.1.4 Example: A Non-Parametric Classifier using Nearest Neighbours
25.1.5 Estimating and Improving Performance
25.2 Building Classifiers from Class Histograms
25.2.1 Finding Skin Pixels using a Classifier
25.2.2 Face Finding Assuming Independent Template Responses
25.3 Feature Selection
25.3.1 Principal Component Analysi
25.3.2 Identifying Individuals with Principal Components Analysis
25.3.3 Canonical Variates
25.4 Neural Networks
25.4.1 Key Ideas
25.4.2 Minimizing the Error
25.4.3 When to Stop Training
25.4.4 Finding Faces using Neural Networks
25.4.5 Convolutional Neural Nets
25.5 The Support Vector Machine
25.5.1 Support Vector Machines for Linearly Separable Datasets
25.5.2 Finding Pedestrians using Support Vector Machines
25.6 Conclusions
25.6.1 Skin Detection
25.6.2 Face Finding
25.6.3 Pedestrian Finding
I Appendix: Backpropagation
II Appendix: Support Vector Machines for Datasets that are notLinearly Separable
Chapter 26 RECOGNITION BY RELATIONS BETWEEN TEMPLATES
26.1 Finding Objects by Voting on Relations between Templates
26.1.1 Describing Image Patche
26.1.2 Voting and a Simple Generative Model
26.1.3 Probabilistic Models for Vot
26.1.4 Voting on Relations
26.1.5 Voting and 3D Objects
26.2 Relational Reasoning using Probabilistic Models and Search
26.2.1 Correspondence and Search
26.2.2 Example: Finding Faces
26.3 Using Classifiers to Prune Search
26.3.1 Identifying Acceptable Assemblies Using Projected Classifiers
26.3.2 Example: Finding People and Horses Using Spatial Relations
26.4 Technique: Hidden Markov Models
26.4.1 Formal Matters
26.4.2 Computing with Hidden Markov Models
26.4.3 Varieties of HMM’s
26.5 Application: HiddenMarkov Models and Sign Language Understanding
26.5.1 Language Models: Sentences from Words
26.6 Application: Finding People with Hidden Markov Models
26.7 Conclusions
26.7.1 Hidden Markov Model
Chapter 27 SMOOTH SURFACES AND THEIR OUTLINES
27.1 Elements of Differential Geometry
27.1.1 Curves
27.1.2 Surfaces
27.1.3 The Shape of Specularities
27.2 Contour Geometry
27.2.1 The Occluding Contour and the Image Contou
27.2.2 The Cusps and Inflections of the Image Contour
27.2.3 Koenderink’s Theorem
27.3 Notes
27.4 Assignments
Chapter 28 ASPECT GRAPHS
28.1 Differential Geometry and Visual Events
28.1.1 The Geometry of the Gauss Map
28.1.2 Asymptotic Curves
28.1.3 The Asymptotic Spherical Map
28.1.4 Local Visual Events
28.1.5 The Bitangent Ray Manifold
28.1.6 Multilocal Visual Events
28.1.7 Remarks
28.2 Computing the Aspect Graph
28.2.1 Step 1: Tracing Visual Events
28.2.2 Step 2: Constructing the Regions
28.2.3 Remaining Steps of the Algorit
28.2.4 An Example
28.3 Aspect Graphs and Object Localization
28.4 Note
28.5 Assignments
Chapter 29 TOWARD CATEGORY-LEVEL OBJECT RECOGNITION
29.1 The State of the Art and its Limitations
29.1.1 Current Approaches to Object Recognition
29.1.2 Limitations
29.1.3 From Templates to Primitive
29.1.4 Models of Object Recognition
29.2 Primitives and Object Recognition
29.2.1 Volumetric Primitives and Part-Whole Decompositions
29.2.2 The Two-Dimensional Case: Ribbons
29.2.3 A Two-Dimensional Recognition System: FORMS
29.2.4 The Three-Dimensional Case: Generalized Cylinders
29.2.5 A Three-Dimensional Recognition System: ACRONYM
29.2.6 Going Further
29.3 Notes
29.4 Assignments
SUBJECT INDEX
BIBLIOGRAPHY
CONTENTS
PREFACE
I
IMAGE FORMATION
1 CAMERAS
1.1 Pinhole Cameras
1.1.1 Perspective Projection
1.1.2 Affine Projection
1.1.3
Spherical Projection
1.2 Cameras with Lenses
1.2.1 First-Order Geometric Optics
1.2.2 Thin Lenses: Geometry
1.2.3 Thin Lenses: Radiometry
1.2.4 Real Lenses
Human Vision: The Structure of the Eye
1.3 Sensing
1.3.1 CCD cameras
1.3.2
Sensor Models
1.4 Notes
1.5 Assignments
2 RADIOMETRY — MEASURING LIGHT
2.1 Light in Space
2.1.1 Foreshortening
2.1.2
2.1.3 Radiance
Solid Angle
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2.2 Light at Surfaces
2.3
Simplifying Assumptions
2.2.1
2.2.2 The Bidirectional Reflectance Distribution Function
Important Special Cases
2.3.1 Radiosity
2.3.2 Directional Hemispheric Reflectance
2.3.3 Lambertian Surfaces and Albedo
2.3.4
2.3.5 The Lambertian + Specular Model
Specular Surfaces
2.4 Quick Reference: Radiometric Terminology for Light
2.5 Quick Reference: Radiometric Properties of Surfaces
2.6 Quick Reference: Important Types of Surface
2.7 Comments
2.8 Assignments
3 SOURCES, SHADOWS AND SHADING
3.1 Radiometric Properties of Light Sources
3.2 Qualitative Radiometry
3.3 Sources and their Effects
3.3.1 Point Sources
3.3.2 Line Sources
3.3.3 Area Sources
3.4 Local Shading Models
3.4.1 Local Shading Models for Point Sources
3.4.2 Area Sources and their Shadows
3.4.3 Ambient Illumination
3.5 Application: Photometric Stereo
3.6
Shape from Normals
3.5.1 Normal and Albedo from Many Views
3.5.2
Interreflections: Global Shading Models
3.6.1 An Interreflection Model
3.6.2
3.6.3 The qualitative effects of interreflections
Solving for Radiosity
3.7 Notes
3.7.1 Local Shading Models
3.7.2
3.7.3 Photometric Stereo
Interreflections
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3.8 Assignments
3.8.1 Exercises
3.8.2 Programming Assignments
4 COLOUR
4.1 The Physics of Colour
4.1.1 Radiometry for Coloured Lights: Spectral Quantities
4.1.2 The Colour of Surfaces
4.1.3 The Colour of Sources
4.2 Human Colour Perception
4.2.1 Colour Matching
4.2.2 Colour Receptors
4.3 Representing Colour
4.3.1 Linear Colour Spaces
4.3.2 Non-linear Colour Spaces
4.3.3
Spatial and Temporal Effects
4.4 A Model for Image Colour
4.4.1 Cameras
4.4.2 A Model for Image Colour
4.4.3 Application: Finding Specularities
4.5 Surface Colour from Image Colour
4.5.1
4.5.2
4.5.3
4.6 Notes
Surface Colour Perception in People
Inferring Lightness
Surface Colour from Finite Dimensional Linear Models
Specularity Finding
4.6.1 Trichromacy and Colour Spaces
4.6.2
4.6.3 Lightness
4.6.4 Colour Constancy
4.6.5 Colour in Recognition
4.7 Assignments
II
IMAGE MODELS
5 GEOMETRIC CAMERA MODELS
5.1 Elements of Analytical Euclidean Geometry
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5.1.1 Coordinate Systems and Homogeneous Coordinates
5.1.2 Coordinate System Changes and Rigid Transformations
5.2 Geometric Camera Parameters
5.2.1
Intrinsic Parameters
5.2.2 Extrinsic Parameters
5.2.3 A Characterization of Perspective Projection Matrices
5.3 Straight Lines and their Projections
5.3.1 Elements of Line Geometry
5.3.2 Projection Equations
5.4 Notes
5.5 Assignments
6 GEOMETRIC CAMERA CALIBRATION
6.1 Least-Squares Parameter Estimation
6.1.1 Linear Least-Squares Methods
6.1.2 Non-Linear Least-Squares Methods
6.2 A Linear Approach to Camera Calibration
6.2.1 Estimation of the Projection Matrix
6.2.2 Estimation of the Intrinsic and Extrinsic Parameters
6.2.3 Degenerate Point Configurations
6.3 Taking Radial Distortion into Account
6.3.1 Estimation of the Projection Matrix
6.3.2 Estimation of the Intrinsic and Extrinsic Parameters
6.3.3 Degenerate Point Configurations
6.4 Using Straight Lines for Calibration
6.5 Analytical Photogrammetry
6.6 An Application: Mobile Robot Localization
6.7 Notes
6.8 Assignments
7 AN INTRODUCTION TO PROBABILITY
7.1 Probability in Discrete Spaces
7.1.1 Probability: the P-function
7.1.2 Conditional Probability
7.1.3 Choosing P
7.2 Probability in Continuous Spaces
7.2.1 Event Structures for Continuous Spaces
7.2.2 Representing P-functions
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7.4 Standard Distributions and Densities
7.5 Probabilistic Inference
7.3 Random Variables
7.3.1 Conditional Probability and Independence
7.3.2 Expectations
7.3.3
Joint Distributions and Marginalization
7.4.1 The Normal Distribution
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7.5.1 The Maximum Likelihood Principle
7.5.2 Priors, Posteriors and Bayes’ rule
7.5.3 Bayesian Inference
7.5.4 Open Issues
7.6 Discussion
III EARLY VISION: ONE IMAGE
8 LINEAR FILTERS
8.1 Linear Filters and Convolution
8.1.1 Convolution
8.2 Shift invariant linear systems
8.2.1 Discrete Convolution
8.2.2 Continuous Convolution
8.2.3 Edge Effects in Discrete Convolutions
8.3 Spatial Frequency and Fourier Transforms
8.3.1 Fourier Transforms
8.4 Sampling and Aliasing
Sampling
8.4.1
8.4.2 Aliasing
8.4.3
Smoothing and Resampling
8.5 Technique: Scale and Image Pyramids
8.5.1 The Gaussian Pyramid
8.5.2 Applications of Scaled Representations
8.5.3
Scale Space
8.6 Discussion
8.6.1 Real Imaging Systems vs Shift-Invariant Linear Systems
8.6.2
8.6.3 Anisotropic Scaling
Scale
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9 EDGE DETECTION
9.1 Noise
9.1.1 Additive Stationary Gaussian Noise
9.1.2 Why Finite Differences Respond to Noise
9.2 Estimating Derivatives
9.2.1 Choosing a Smoothing Filter
9.2.2 Why Smooth with a Gaussian?
9.2.3 Derivative of Gaussian Filters
9.3 Detecting Edges
9.3.1 Using the Laplacian to Detect Edges
9.3.2 Gradient Based Edge Detectors
9.3.3 Technique: Orientation Representations and Corners
9.4 Commentary
10 FILTERS AND FEATURES
10.1 Filters as Templates
10.1.1 Convolution as a Dot Product
10.1.2 Changing Basis
10.2 Technique: Normalised Correlation and Finding Patterns
10.2.1 Controlling the Television by Finding Hands by Normalised
Correlation
10.3 Human Vision: Filters and Primate Early Vision
10.3.1 The Visual Pathway
10.3.2 The Response of Retinal Cells
10.3.3 The Lateral Geniculate Nucleus
10.3.4 The Visual Cortex
10.3.5 A Model of Early Spatial Vision
10.4 Advanced Smoothing Strategies and Non-linear Filters
10.4.1 More Noise Models
10.4.2 Robust Estimates
10.4.3 Median Filters
10.4.4 Mathematical morphology: erosion and dilation
10.5 Commentary
11 TEXTURE
11.1 Representing Texture
11.1.1 Extracting Image Structure with Filter Banks
11.2 Analysis (and Synthesis) Using Oriented Pyramids
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11.3 Application: Synthesizing Textures for Rendering
11.2.1 The Laplacian Pyramid
11.2.2 Filters in the Spatial Frequency Domain
11.2.3 Oriented Pyramids
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11.3.1 Homogeneity
11.3.2 Synthesis by Matching Histograms of Filter Responses
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11.3.4 Synthesis by Sampling Local Models
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11.5.1 Filters, Pyramids and Efficiency
11.5.2 Texture Synthesis
11.5.3 Shape from Texture
11.4 Shape from Texture
11.4.1 Shape from Texture for Planes
11.4.2 Shape from Texture for Curved Surfaces
11.5 Notes
IV EARLY VISION: MULTIPLE IMAGES
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12 THE GEOMETRY OF MULTIPLE VIEWS
12.1 Two Views
12.1.1 Epipolar Geometry
12.1.2 The Calibrated Case
12.1.3 Small Motions
12.1.4 The Uncalibrated Case
12.1.5 Weak Calibration
12.2 Three Views
12.2.1 Trifocal Geometry
12.2.2 The Calibrated Case
12.2.3 The Uncalibrated Case
12.2.4 Estimation of the Trifocal Tensor
12.3 More Views
12.4 Notes
12.5 Assignments
13 STEREOPSIS
13.1 Reconstruction
13.1.1 Camera Calibration
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13.1.2 Image Rectification
Human Vision: Stereopsis
13.2 Binocular Fusion
13.2.1 Correlation
13.2.2 Multi-Scale Edge Matching
13.2.3 Dynamic Programming
13.3 Using More Cameras
13.3.1 Trinocular Stereo
13.3.2 Multiple-Baseline Stereo
13.4 Notes
13.5 Assignments
14 AFFINE STRUCTURE FROM MOTION
14.1 Elements of Affine Geometry
14.2 Affine Structure from Two Images
14.2.1 The Affine Structure-from-Motion Theorem
14.2.2 Rigidity and Metric Constraints
14.3 Affine Structure from Multiple Images
14.3.1 The Affine Structure of Affine Image Sequences
Technique: Singular Value Decomposition
14.3.2 A Factorization Approach to Affine Motion Analysis
14.4 From Affine to Euclidean Images
14.4.1 Euclidean Projection Models
14.4.2 From Affine to Euclidean Motion
14.5 Affine Motion Segmentation
14.5.1 The Reduced Echelon Form of the Data Matrix
14.5.2 The Shape Interaction Matrix
14.6 Notes
14.7 Assignments
15 PROJECTIVE STRUCTURE FROM MOTION
15.1 Elements of Projective Geometry
15.1.1 Projective Bases and Projective Coordinates
15.1.2 Projective Transformations
15.1.3 Affine and Projective Spaces
15.1.4 Hyperplanes and Duality
15.1.5 Cross-Ratios
15.1.6 Application: Parameterizing the Fundamental Matrix
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