Fundamentals of Digital Image Processing: A Practical Approach with Examples in Matlab -- Contents -- Preface -- Using the book website -- 1 Representation -- 1.1 What is an image? -- 1.1.1 Image layout -- 1.1.2 Image colour -- 1.2 Resolution and quantization -- 1.2.1 Bit-plane splicing -- 1.3 Image formats -- 1.3.1 Image data types -- 1.3.2 Image compression -- 1.4 Colour spaces -- 1.4.1 RGB -- 1.4.1.1 RGB to grey-scale image conversion -- 1.4.2 Perceptual colour space -- 1.5 Images in Matlab -- 1.5.1 Reading, writing and querying images -- 1.5.2 Basic display of images -- 1.5.3 Accessing pixel values -- 1.5.4 Converting image types -- Exercises -- 2 Formation -- 2.1 How is an image formed? -- 2.2 The mathematics of image formation -- 2.2.1 Introduction -- 2.2.2 Linear imaging systems -- 2.2.3 Linear superposition integral -- 2.2.4 The Dirac delta or impulse function -- 2.2.5 The point-spread function -- 2.2.6 Linear shift-invariant systems and the convolution integral -- 2.2.7 Convolution: its importance and meaning -- 2.2.8 Multiple convolution: N imaging elements in a linear shift-invariant system -- 2.2.9 Digital convolution -- 2.3 The engineering of image formation -- 2.3.1 The camera -- 2.3.2 The digitization process -- 2.3.2.1 Quantization -- 2.3.2.2 Digitization hardware -- 2.3.2.3 Resolution versus performance -- 2.3.3 Noise -- Exercises -- 3 Pixels -- 3.1 What is a pixel? -- 3.2 Operations upon pixels -- 3.2.1 Arithmetic operations on images -- 3.2.1.1 Image addition and subtraction -- 3.2.1.2 Image multiplication and division -- 3.2.2 Logical operations on images -- 3.2.3 Thresholding -- 3.3 Point-based operations on images -- 3.3.1 Logarithmic transform -- 3.3.2 Exponential transform -- 3.3.3 Power-law (gamma) transform -- 3.3.3.1 Application: gamma correction -- 3.4 Pixel distributions: histograms.

3.4.1 Histograms for threshold selection -- 3.4.2 Adaptive thresholding -- 3.4.3 Contrast stretching -- 3.4.4 Histogram equalization -- 3.4.4.1 Histogram equalization theory -- 3.4.4.2 Histogram equalization theory: discrete case -- 3.4.4.3 Histogram equalization in practice -- 3.4.5 Histogram matching -- 3.4.5.1 Histogram matching theory -- 3.4.5.2 Histogram matching theory: discrete case -- 3.4.5.3 Histogram matching in practice -- 3.4.6 Adaptive histogram equalization -- 3.4.7 Histogram operations on colour images -- Exercises -- 4 Enhancement -- 4.1 Why perform enhancement? -- 4.1.1 Enhancement via image filtering -- 4.2 Pixel neighbourhoods -- 4.3 Filter kernels and the mechanics of linear filtering -- 4.3.1 Nonlinear spatial filtering -- 4.4 Filtering for noise removal -- 4.4.1 Mean filtering -- 4.4.2 Median filtering -- 4.4.3 Rank filtering -- 4.4.4 Gaussian filtering -- 4.5 Filtering for edge detection -- 4.5.1 Derivative filters for discontinuities -- 4.5.2 First-order edge detection -- 4.5.2.1 Linearly separable filtering -- 4.5.3 Second-order edge detection -- 4.5.3.1 Laplacian edge detection -- 4.5.3.2 Laplacian of Gaussian -- 4.5.3.3 Zero-crossing detector -- 4.6 Edge enhancement -- 4.6.1 Laplacian edge sharpening -- 4.6.2 The unsharp mask filter -- Exercises -- 5 Fourier transforms and frequency-domain processing -- 5.1 Frequency space: a friendly introduction -- 5.2 Frequency space: the fundamental idea -- 5.2.1 The Fourier series -- 5.3 Calculation of the Fourier spectrum -- 5.4 Complex Fourier series -- 5.5 The 1-D Fourier transform -- 5.6 The inverse Fourier transform and reciprocity -- 5.7 The 2-D Fourier transform -- 5.8 Understanding the Fourier transform: frequency-space filtering -- 5.9 Linear systems and Fourier transforms -- 5.10 The convolution theorem -- 5.11 The optical transfer function.

5.12 Digital Fourier transforms: the discrete fast Fourier transform -- 5.13 Sampled data: the discrete Fourier transform -- 5.14 The centred discrete Fourier transform -- 6 Image restoration -- 6.1 Imaging models -- 6.2 Nature of the point-spread function and noise -- 6.3 Restoration by the inverse Fourier filter -- 6.4 The Wiener-Helstrom filter -- 6.5 Origin of the Wiener-Helstrom filter -- 6.6 Acceptable solutions to the imaging equation -- 6.7 Constrained deconvolution -- 6.8 Estimating an unknown point-spread function or optical transfer function -- 6.9 Blind deconvolution -- 6.10 Iterative deconvolution and the Lucy-Richardson algorithm -- 6.11 Matrix formulation of image restoration -- 6.12 The standard least-squares solution -- 6.13 Constrained least-squares restoration -- 6.14 Stochastic input distributions and Bayesian estimators -- 6.15 The generalized Gauss-Markov estimator -- 7 Geometry -- 7.1 The description of shape -- 7.2 Shape-preserving transformations -- 7.3 Shape transformation and homogeneous coordinates -- 7.4 The general 2-D affine transformation -- 7.5 Affine transformation in homogeneous coordinates -- 7.6 The procrustes transformation -- 7.7 Procrustes alignment -- 7.8 The projective transform -- 7.9 Nonlinear transformations -- 7.10 Warping: the spatial transformation of an image -- 7.11 Overdetermined spatial transformations -- 7.12 The piecewise warp -- 7.13 The piecewise affine warp -- 7.14 Warping: forward and reverse mapping -- 8 Morphological processing -- 8.1 Introduction -- 8.2 Binary images: foreground, background and connectedness -- 8.3 Structuring elements and neighbourhoods -- 8.4 Dilation and erosion -- 8.5 Dilation, erosion and structuring elements within Matlab -- 8.6 Structuring element decomposition and Matlab -- 8.7 Effects and uses of erosion and dilation.

8.7.1 Application of erosion to particle sizing -- 8.8 Morphological opening and closing -- 8.8.1 The rolling-ball analogy -- 8.9 Boundary extraction -- 8.10 Extracting connected components -- 8.11 Region filling -- 8.12 The hit-or-miss transformation -- 8.12.1 Generalization of hit-or-miss -- 8.13 Relaxing constraints in hit-or-miss: 'don't care' pixels -- 8.13.1 Morphological thinning -- 8.14 Skeletonization -- 8.15 Opening by reconstruction -- 8.16 Grey-scale erosion and dilation -- 8.17 Grey-scale structuring elements: general case -- 8.18 Grey-scale erosion and dilation with flat structuring elements -- 8.19 Grey-scale opening and closing -- 8.20 The top-hat transformation -- 8.21 Summary -- Exercises -- 9 Features -- 9.1 Landmarks and shape vectors -- 9.2 Single-parameter shape descriptors -- 9.3 Signatures and the radial fourier expansion -- 9.4 Statistical moments as region descriptors -- 9.5 Texture features based on statistical measures -- 9.6 Principal component analysis -- 9.7 Principal component analysis: an illustrative example -- 9.8 Theory of principal component analysis: version 1 -- 9.9 Theory of principal component analysis: version 2 -- 9.10 Principal axes and principal components -- 9.11 Summary of properties of principal component analysis -- 9.12 Dimensionality reduction: the purpose of principal component analysis -- 9.13 Principal components analysis on an ensemble of digital images -- 9.14 Representation of out-of-sample examples using principal component analysis -- 9.15 Key example: eigenfaces and the human face -- 10 Image segmentation -- 10.1 Image segmentation -- 10.2 Use of image properties and features in segmentation -- 10.3 Intensity thresholding -- 10.3.1 Problems with global thresholding -- 10.4 Region growing and region splitting -- 10.5 Split-and-merge algorithm -- 10.6 The challenge of edge detection.

10.7 The laplacian of Gaussian and difference of Gaussians filters -- 10.8 The Canny edge detector -- 10.9 Interest operators -- 10.10 Watershed segmentation -- 10.11 Segmentation functions -- 10.12 Image segmentation with markov random fields -- 10.12.1 Parameter estimation -- 10.12.2 Neighbourhood weighting parameter θn -- 10.12.3 Minimizing U(x