1. Introduction

1.1 Overview

1.2 Human and computer vision

1.3 The human vision system

1.3.1 The eye

1.3.2 The neural system

1.3.3 Processing

1.4 Computer vision systems

1.4.1 Cameras

1.4.2 Computer interfaces

1.5 Processing images

1.5.1 Processing

1.5.2 Hello Python, hello images!

1.5.3 Mathematical tools

1.5.4 Hello Matlab

1.6 Associated literature

1.6.1 Journals, magazines and conferences

1.6.2 Textbooks

1.6.3 The web

1.7 Conclusions

References

2. Images, sampling and frequency domain processing

2.1 Overview

2.2 Image formation

2.3 The Fourier Transform

2.4 The sampling criterion

2.5 The discrete Fourier Transform

2.5.1 One-dimensional transform

2.5.2 Two-dimensional transform

2.6 Properties of the Fourier Transform

2.6.1 Shift invariance

2.6.2 Rotation

2.6.3 Frequency scaling

2.6.4 Superposition (linearity)

2.6.5 The importance of phase

2.7 Transforms other than Fourier

2.7.1 Discrete cosine transform

2.7.2 Discrete Hartley Transform

2.7.3 Introductory wavelets

2.7.3.1 Gabor Wavelet

2.7.3.2 Haar Wavelet

2.7.4 Other transforms

2.8 Applications using frequency domain properties

2.9 Further reading

References

3. Image processing

3.1 Overview

3.2 Histograms

3.3 Point operators

3.3.1 Basic point operations

3.3.2 Histogram normalisation

3.3.3 Histogram equalisation

3.3.4 Thresholding

3.4 Group operations

3.4.1 Template convolution

3.4.2 Averaging operator

3.4.3 On different template size

3.4.4 Template convolution via the Fourier transform

3.4.5 Gaussian averaging operator

3.4.6 More on averaging

3.5 Other image processing operators

3.5.1 Median filter

3.5.2 Mode filter

3.5.3 Nonlocal means

3.5.4 Bilateral filtering

3.5.5 Anisotropic diffusion

3.5.6 Comparison of smoothing operators

3.5.7 Force field transform

3.5.8 Image ray transform

3.6 Mathematical morphology

3.6.1 Morphological operators

3.6.2 Grey level morphology

3.6.3 Grey level erosion and dilation

3.6.4 Minkowski operators

3.7 Further reading

References

4. Low-level feature extraction (including edge detection)

4.1 Overview

4.2 Edge detection

4.2.1 First-order edge detection operators

4.2.1.1 Basic operators

4.2.1.2 Analysis of the basic operators

4.2.1.3 Prewitt edge detection operator

4.2.1.4 Sobel edge detection operator

4.2.1.5 The Canny edge detector

4.2.2 Second-order edge detection operators

4.2.2.1 Motivation

4.2.2.2 Basic operators: The Laplacian

4.2.2.3 The Marr–Hildreth operator

4.2.3 Other edge detection operators

4.2.4 Comparison of edge detection operators

4.2.5 Further reading on edge detection

4.3 Phase congruency

4.4 Localised feature extraction

4.4.1 Detecting image curvature (corner extraction)

4.4.1.1 Definition of curvature

4.4.1.2 Computing differences in edge direction

4.4.1.3 Measuring curvature by changes in intensity (differentiation)

4.4.1.4 Moravec and Harris detectors

4.4.1.5 Further reading on curvature

4.4.2 Feature point detection; region/patch analysis

4.4.2.1 Scale invariant feature transform

4.4.2.2 Speeded up robust features

4.4.2.3 FAST, ORB, FREAK, LOCKY and other keypoint detectors

4.4.2.4 Other techniques and performance issues

4.4.3 Saliency

4.4.3.1 Basic saliency

4.4.3.2 Context aware saliency

4.4.3.3 Other saliency operators

4.5 Describing image motion

4.5.1 Area-based approach

4.5.2 Differential approach

4.5.3 Recent developments: deep flow, epic flow and extensions

4.5.4 Analysis of optical flow

4.6 Further reading

References

5. High-level feature extraction: fixed shape matching

5.1 Overview

5.2 Thresholding and subtraction

5.3 Template matching

5.3.1 Definition

5.3.2 Fourier transform implementation

5.3.3 Discussion of template matching

5.4 Feature extraction by low-level features

5.4.1 Appearance-based approaches

5.4.1.1 Object detection by templates

5.4.1.2 Object detection by combinations of parts

5.4.2 Distribution-based descriptors

5.4.2.1 Description by interest points (SIFT, SURF, BRIEF)

5.4.2.2 Characterising object appearance and shape

5.5 Hough transform

5.5.1 Overview

5.5.2 Lines

5.5.3 HT for circles

5.5.4 HT for ellipses

5.5.5 Parameter space decomposition

5.5.5.1 Parameter space reduction for lines

5.5.5.2 Parameter space reduction for circles

5.5.5.3 Parameter space reduction for ellipses

5.5.6 Generalised Hough transform

5.5.6.1 Formal definition of the GHT

5.5.6.2 Polar definition

5.5.6.3 The GHT technique

5.5.6.4 Invariant GHT

5.5.7 Other extensions to the HT

5.6 Further reading

References

6. High-level feature extraction: deformable shape analysis

6.1 Overview

6.2 Deformable shape analysis

6.2.1 Deformable templates

6.2.2 Parts-based shape analysis

6.3 Active contours (snakes)

6.3.1 Basics

6.3.2 The Greedy Algorithm for snakes

6.3.3 Complete (Kass) Snake implementation

6.3.4 Other Snake approaches

6.3.5 Further Snake developments

6.3.6 Geometric active contours (Level Set-Based Approaches)

6.4 Shape Skeletonisation

6.4.1 Distance transforms

6.4.2 Symmetry

6.5 Flexible shape models – active shape and active appearance

6.6 Further reading

References

7. Object description

7.1 Overview and invariance requirements

7.2 Boundary descriptions

7.2.1 Boundary and region

7.2.2 Chain codes

7.2.3 Fourier descriptors

7.2.3.1 Basis of Fourier descriptors

7.2.3.2 Fourier expansion

7.2.3.3 Shift invariance

7.2.3.4 Discrete computation

7.2.3.5 Cumulative angular function

7.2.3.6 Elliptic Fourier descriptors

7.2.3.7 Invariance

7.3 Region descriptors

7.3.1 Basic region descriptors

7.3.2 Moments

7.3.2.1 Definition and properties

7.3.2.2 Geometric moments

7.3.2.3 Geometric complex moments and centralised moments

7.3.2.4 Rotation and scale invariant moments

7.3.2.5 Zernike moments

7.3.2.6 Tchebichef moments

7.3.2.7 Krawtchouk moments

7.3.2.8 Other moments

7.4 Further reading

References

8. Region-based analysis

8.1 Overview

8.2 Region-based analysis

8.2.1 Watershed transform

8.2.2 Maximally stable extremal regions

8.2.3 Superpixels

8.2.3.1 Basic techniques and normalised cuts

8.2.3.2 Simple linear iterative clustering

8.3 Texture description and analysis

8.3.1 What is texture?

8.3.2 Performance requirements

8.3.3 Structural approaches

8.3.4 Statistical approaches

8.3.4.1 Co-occurrence matrix

8.3.4.2 Learning-based approaches

8.3.5 Combination approaches

8.3.6 Local binary patterns

8.3.7 Other approaches

8.3.8 Segmentation by texture

8.4 Further reading

References

9. Moving object detection and description

9.1 Overview

9.2 Moving object detection

9.2.1 Basic approaches

9.2.1.1 Detection by subtracting the background

9.2.1.2 Improving quality by morphology

9.2.2 Modelling and adapting to the (static) background

9.2.3 Background segmentation by thresholding

9.2.4 Problems and advances

9.3 Tracking moving features

9.3.1 Tracking moving objects

9.3.2 Tracking by local search

9.3.3 Problems in tracking

9.3.4 Approaches to tracking

9.3.5 MeanShift and Camshift

9.3.5.1 Kernel-based density estimation

9.3.5.2 MeanShift tracking 456

9.3.5.3 Camshift technique 461

9.3.6 Other approaches 465

9.4 Moving feature extraction and description 468

9.4.1 Moving (biological) shape analysis 468

9.4.2 Space–time interest points 470

9.4.3 Detecting moving shapes by shape matching in

image sequences 470

9.4.4 Moving shape description 474

9.5 Further reading 477

References 478

Contents xv

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10. Camera geometry fundamentals 483

10.1 Overview 483

10.2 Projective space 483

10.2.1 Homogeneous co-ordinates and projective

geometry 484

10.2.2 Representation of a line, duality and ideal points 485

10.2.3 Transformations in the projective space 487

10.2.4 Computing a planar homography 490

10.3 The perspective camera 493

10.3.1 Perspective camera model 494

10.3.2 Parameters of the perspective camera model 498

10.3.3 Computing a projection from an image 498

10.4 Affine camera

10.4.1 Affine camera model

10.4.2 Affine camera model and the perspective projection

10.4.3 Parameters of the affine camera model

10.5 Weak perspective model

10.6 Discussion

10.7 Further reading

References

11. Colour images

11.1 Overview

11.2 Colour image theory

11.2.1 Colour images

11.2.2 Tristimulus theory

11.2.3 The colourimetric equation

11.2.4 Luminosity function

11.3 Perception-based colour models: CIE RGB and CIE XYZ

11.3.1 CIE RGB colour model: Wright–Guild data

11.3.2 CIE RGB colour matching functions

11.3.3 CIE RGB chromaticity diagram and chromaticity co-ordinates

11.3.4 CIE XYZ colour model

11.3.5 CIE XYZ colour matching functions

11.3.6 XYZ chromaticity diagram

11.3.7 Uniform colour spaces: CIE LUV and CIE LAB

11.4 Additive and subtractive colour models

11.4.1 RGB and CMY

11.4.2 Transformation between RGB models

11.4.3 Transformation between RGB and CMY models

11.5 Luminance and chrominance colour models

11.5.1 YUV, YIQ and YCbCr models

11.5.2 Luminance and gamma correction

11.5.3 Chrominance

11.5.4 Transformations between YUV, YIQ and RGB colour models

11.5.5 Colour model for component video: YPbPr

11.5.6 Colour model for digital video: YCbCr

11.6 Additive perceptual colour models

11.6.1 The HSV and HLS colour models

11.6.2 The hexagonal model: HSV

11.6.3 The triangular model: HLS

11.6.4 Transformation between HLS and RGB

11.7 More colour models

References

12. Distance, classification and learning

12.1 Overview

12.2 Basis of classification and learning

12.3 Distance and classification

12.3.1 Distance measures

12.3.1.1 Manhattan and Euclidean Ln norms

12.3.1.2 Mahalanobis, Bhattacharrya and Matusita

12.3.1.3 Histogram intersection, Chi2 (c2) and the Earth Mover’s distance

12.3.2 The k-nearest neighbour for classification

12.4 Neural networks and Support Vector Machines

12.5 Deep learning

12.5.1 Basis of deep learning

12.5.2 Major deep learning architectures

12.5.3 Deep learning for feature extraction

12.5.4 Deep learning performance evaluation

12.6 Further reading

References