Fundamentals of Digital Image Processing

Dr Chris Solomon, Applied Optics Group, School of Physical Sciences, The University of Kent, Canterbury, Kent, UK. Dr Stuart Gibson, VisionMetric, Canterbury, Kent, UK.

• Preface xiUsing the book website xv1 Representation 11.1 What is an image? 11.1.1 Image layout 11.1.2 Image colour 21.2 Resolution and quantization 31.2.1 Bit-plane splicing 41.3 Image formats 51.3.1 Image data types 61.3.2 Image compression 71.4 Colour spaces 91.4.1 Rgb 101.4.1.1 RGB to grey-scale image conversion 111.4.2 Perceptual colour space 121.5 Images in Matlab 141.5.1 Reading, writing and querying images 141.5.2 Basic display of images 151.5.3 Accessing pixel values 161.5.4 Converting image types 17Exercises 182 Formation 212.1 How is an image formed? 212.2 The mathematics of image formation 222.2.1 Introduction 222.2.2 Linear imaging systems 232.2.3 Linear superposition integral 242.2.4 The Dirac delta or impulse function 252.2.5 The point-spread function 282.2.6 Linear shift-invariant systems and the convolution integral 292.2.7 Convolution: its importance and meaning 302.2.8 Multiple convolution: N imaging elements in a linear shift-invariant system 342.2.9 Digital convolution 342.3 The engineering of image formation 372.3.1 The camera 382.3.2 The digitization process 402.3.2.1 Quantization 402.3.2.2 Digitization hardware 422.3.2.3 Resolution versus performance 432.3.3 Noise 44Exercises 463 Pixels 493.1 What is a pixel? 493.2 Operations upon pixels 503.2.1 Arithmetic operations on images 513.2.1.1 Image addition and subtraction 513.2.1.2 Multiplication and division 533.2.2 Logical operations on images 543.2.3 Thresholding 553.3 Point-based operations on images 573.3.1 Logarithmic transform 573.3.2 Exponential transform 593.3.3 Power-law (gamma) transform 613.3.3.1 Application: gamma correction 623.4 Pixel distributions: histograms 633.4.1 Histograms for threshold selection 653.4.2 Adaptive thresholding 663.4.3 Contrast stretching 673.4.4 Histogram equalization 693.4.4.1 Histogram equalization theory 693.4.4.2 Histogram equalization theory: discrete case 703.4.4.3 Histogram equalization in practice 713.4.5 Histogram matching 733.4.5.1 Histogram-matching theory 733.4.5.2 Histogram-matching theory: discrete case 743.4.5.3 Histogram matching in practice 753.4.6 Adaptive histogram equalization 763.4.7 Histogram operations on colour images 79Exercises 814 Enhancement 854.1 Why perform enhancement? 854.1.1 Enhancement via image filtering 854.2 Pixel neighbourhoods 864.3 Filter kernels and the mechanics of linear filtering 874.3.1 Nonlinear spatial filtering 904.4 Filtering for noise removal 904.4.1 Mean filtering 914.4.2 Median filtering 924.4.3 Rank filtering 944.4.4 Gaussian filtering 954.5 Filtering for edge detection 974.5.1 Derivative filters for discontinuities 974.5.2 First-order edge detection 994.5.2.1 Linearly separable filtering 1014.5.3 Second-order edge detection 1024.5.3.1 Laplacian edge detection 1024.5.3.2 Laplacian of Gaussian 1034.5.3.3 Zero-crossing detector 1044.6 Edge enhancement 1054.6.1 Laplacian edge sharpening 1054.6.2 The unsharp mask filter 107Exercises 1095 Fourier transforms and frequency-domain processing 1135.1 Frequency space: a friendly introduction 1135.2 Frequency space: the fundamental idea 1145.2.1 The Fourier series 1155.3 Calculation of the Fourier spectrum 1185.4 Complex Fourier series 1185.5 The 1-D Fourier transform 1195.6 The inverse Fourier transform and reciprocity 1215.7 The 2-D Fourier transform 1235.8 Understanding the Fourier transform: frequency-space filtering 1265.9 Linear systems and Fourier transforms 1295.10 The convolution theorem 1295.11 The optical transfer function 1315.12 Digital Fourier transforms: the discrete fast Fourier transform 1345.13 Sampled data: the discrete Fourier transform 1355.14 The centred discrete Fourier transform 1366 Image restoration 1416.1 Imaging models 1416.2 Nature of the point-spread function and noise 1426.3 Restoration by the inverse Fourier filter 1436.4 The Wiener–Helstrom Filter 1466.5 Origin of the Wiener–Helstrom filter 1476.6 Acceptable solutions to the imaging equation 1516.7 Constrained deconvolution 1516.8 Estimating an unknown point-spread function or optical transfer function 1546.9 Blind deconvolution 1566.10 Iterative deconvolution and the Lucy–Richardson algorithm 1586.11 Matrix formulation of image restoration 1616.12 The standard least-squares solution 1626.13 Constrained least-squares restoration 1636.14 Stochastic input distributions and Bayesian estimators 1656.15 The generalized Gauss–Markov estimator 1657 Geometry 1697.1 The description of shape 1697.2 Shape-preserving transformations 1707.3 Shape transformation and homogeneous coordinates 1717.4 The general 2-D affine transformation 1737.5 Affine transformation in homogeneous coordinates 1747.6 The Procrustes transformation 1757.7 Procrustes alignment 1767.8 The projective transform 1807.9 Nonlinear transformations 1847.10 Warping: the spatial transformation of an image 1867.11 Overdetermined spatial transformations 1897.12 The piecewise warp 1917.13 The piecewise affine warp 1917.14 Warping: forward and reverse mapping 1948 Morphological processing 1978.1 Introduction 1978.2 Binary images: foreground, background and connectedness 1978.3 Structuring elements and neighbourhoods 1988.4 Dilation and erosion 2008.5 Dilation, erosion and structuring elements within Matlab 2018.6 Structuring element decomposition and Matlab 2028.7 Effects and uses of erosion and dilation 2048.7.1 Application of erosion to particle sizing 2078.8 Morphological opening and closing 2098.8.1 The rolling-ball analogy 2108.9 Boundary extraction 2128.10 Extracting connected components 2138.11 Region filling 2158.12 The hit-or-miss transformation 2168.12.1 Generalization of hit-or-miss 2198.13 Relaxing constraints in hit-or-miss: ‘don’t care’ pixels 2208.13.1 Morphological thinning 2228.14 Skeletonization 2228.15 Opening by reconstruction 2248.16 Grey-scale erosion and dilation 2278.17 Grey-scale structuring elements: general case 2278.18 Grey-scale erosion and dilation with flat structuring elements 2288.19 Grey-scale opening and closing 2298.20 The top-hat transformation 2308.21 Summary 231Exercises 2339 Features 2359.1 Landmarks and shape vectors 2359.2 Single-parameter shape descriptors 2379.3 Signatures and the radial Fourier expansion 2399.4 Statistical moments as region descriptors 2439.5 Texture features based on statistical measures 2469.6 Principal component analysis 2479.7 Principal component analysis: an illustrative example 2479.8 Theory of principal component analysis: version 1 2509.9 Theory of principal component analysis: version 2 2519.10 Principal axes and principal components 2539.11 Summary of properties of principal component analysis 2539.12 Dimensionality reduction: the purpose of principal component analysis 2569.13 Principal components analysis on an ensemble of digital images 2579.14 Representation of out-of-sample examples using principal component analysis 2579.15 Key example: eigenfaces and the human face 25910 Image Segmentation 26310.1 Image segmentation 26310.2 Use of image properties and features in segmentation 26310.3 Intensity thresholding 26510.3.1 Problems with global thresholding 26610.4 Region growing and region splitting 26710.5 Split-and-merge algorithm 26710.6 The challenge of edge detection 27010.7 The Laplacian of Gaussian and difference of Gaussians filters 27010.8 The Canny edge detector 27110.9 Interest operators 27410.10 Watershed segmentation 27910.11 Segmentation functions 28010.12 Image segmentation with Markov random fields 28610.12.1 Parameter estimation 28810.12.2 Neighbourhood weighting parameter u n 28910.12.3 Minimizing U(x | y): the iterated conditional modes algorithm 29011 Classification 29111.1 The purpose of automated classification 29111.2 Supervised and unsupervised classification 29211.3 Classification: a simple example 29211.4 Design of classification systems 29411.5 Simple classifiers: prototypes and minimum distance criteria 29611.6 Linear discriminant functions 29711.7 Linear discriminant functions in N dimensions 30111.8 Extension of the minimum distance classifier and the Mahalanobis distance 30211.9 Bayesian classification: definitions 30311.10 The Bayes decision rule 30411.11 The multivariate normal density 30611.12 Bayesian classifiers for multivariate normal distributions 30711.12.1 The Fisher linear discriminant 31011.12.2 Risk and cost functions 31111.13 Ensemble classifiers 31211.13.1 Combining weak classifiers: the AdaBoost method 31311.14 Unsupervised learning: k-means clustering 313Further reading 317Index 319

“Given the timely topic and its user-friendly structure, this book can therefore target a suite of users, from students to experienced researchers willing to integrate the science of image processing to strengthen their research.”  (Ethology Ecology & Evolution, 1 May 2013)"For undergraduate and graduate students as well as professionals, Solomon (physical sciences, U. of Kent, UK) and Breckon (engineering, Cranfield U., UK) provide a simple introduction to the science of modern image processing and pattern recognition, their key concepts and techniques, and theory." (Booknews, 1 April 2011)