Handbook of Image Processing and Computer Vision: Volume 2: From Image to Pattern

Preface
Acknowledgements
Contents
1 Local Operations: Edging
	1.1 Basic Definitions
	1.2 Gradient Filter
	1.3 Approximation of the Gradient Filter
	1.4 Roberts Operator
	1.5 Gradient Image Thresholding
	1.6 Sobel Operator
	1.7 Prewitt Operator
	1.8 Frei & Chen Operator
	1.9 Comparison of LED Operators
	1.10 Directional Gradient Operator
	1.11 Gaussian Derivative Operator (DroG)
	1.12 Laplacian Operator
	1.13 Laplacian of Gaussian (LoG)
	1.14 Difference of Gaussians (DoG)
	1.15 Second-Directional Derivative Operator
	1.16 Canny Edge Operator
		1.16.1 Canny Algorithm
	1.17 Point Extraction
	1.18 Line Extraction
	1.19 High-Pass Filtering
		1.19.1 Ideal High-Pass Filter (IHPF)
		1.19.2 Butterworth High-Pass Filter (BHPF)
		1.19.3 Gaussian High-Pass Filter (GHPF)
	1.20 Ideal Band-Stop Filter (IBSF)
		1.20.1 Butterworth and Gaussian Band-Stop Filter
	1.21 Band-Pass Filter (BPF)
		1.21.1 Ideal Band-Pass Filter (IBPF)
		1.21.2 Butterworth and Gaussian Band-Pass Filter
		1.21.3 Difference of Gaussian Band-Pass Filter
		1.21.4 Laplacian Filter in the Frequency Domain
	1.22 Sharpening Filters
		1.22.1 Sharpening Linear Filters
		1.22.2 Unsharp Masking
		1.22.3 Sharpening High-Boost Filter
		1.22.4 Sharpening Filtering in the Frequency Domain
		1.22.5 Homomorphic Filter
2 Fundamental Linear Transforms
	2.1 Introduction
	2.2 One-Dimensional Discrete Linear Transformation
		2.2.1 Unitary Transforms
		2.2.2 Orthogonal Transforms
		2.2.3 Orthonormal Transforms
		2.2.4 Example of One-Dimensional Unitary Transformation
	2.3 Two-Dimensional Discrete Linear Transformation
		2.3.1 Example of a Two-Dimensional Unitary Transformation
	2.4 Observations on Unitary Transformations
		2.4.1 Properties of Unitary Transformations
	2.5 Sinusoidal Transforms
	2.6 Discrete Cosine Transform (DCT)
	2.7 Discrete Sine Transform (DST)
	2.8 Discrete Hartley Transform (DHT)
	2.9 Transform with Rectangular Functions
		2.9.1 Discrete Transform of Hadamard—DHaT
		2.9.2 Discrete Transform of Walsh (DWHT)
		2.9.3 Slant Transform
		2.9.4 Haar Transform
	2.10 Transform Based on the Eigenvectors and Eigenvalues
		2.10.1 Principal Component Analysis (PCA)
		2.10.2 PCA/KLT for Data Compression
		2.10.3 Computation of the Principal Axes of a Two-Dimensional Object
		2.10.4 Dimensionality Reduction
		2.10.5 Calculation of Significant Components in Multispectral Images
		2.10.6 Eigenface—Face Recognition
	2.11 Singular Value Decomposition SVD Transform
	2.12 Wavelet Transform
		2.12.1 Continuous Wavelet Transforms—CWT
		2.12.2 Continuous Wavelet Transform—2D CWT
		2.12.3 Wavelet Transform as Band-pass Filtering
		2.12.4 Discrete Wavelet Transform—DWT
		2.12.5 Fast Wavelet Transform—FWT
		2.12.6 Discrete Wavelet Transform 2D—DWT2
		2.12.7 Biorthogonal Wavelet Transform
		2.12.8 Applications of the Discrete Wavelet Transform
	2.13 Summary of the Chapter
3 Geometric Transformations
	3.1 Introduction
	3.2 Homogeneous Coordinates
	3.3 Geometric Operator
		3.3.1 Translation
		3.3.2 Magnification or Reduction
		3.3.3 Rotation
		3.3.4 Skew or Shear
		3.3.5 Specular
		3.3.6 Transposed
		3.3.7 Coordinate Systems and Homogeneous Coordinates
		3.3.8 Elementary Homogeneous Geometric Transformations
	3.4 Geometric Affine Transformations
		3.4.1 Affine Transformation of Similarity
		3.4.2 Generalized Affine Transformation
		3.4.3 Elementary Affine Transformations
	3.5 Separability of Transformations
	3.6 Homography Transformation
		3.6.1 Applications of the Homography Transformation
	3.7 Perspective Transformation
	3.8 Geometric Transformations for Image Registration
	3.9 Nonlinear Geometric Transformations
	3.10 Geometric Transformation and Resampling
		3.10.1 Ideal Interpolation
		3.10.2 Zero-Order Interpolation (Nearest-Neighbor)
		3.10.3 Linear Interpolation of the First Order
		3.10.4 Biquadratic Interpolation
		3.10.5 Bicubic Interpolation
		3.10.6 B-Spline Interpolation
		3.10.7 Interpolation by Least Squares Approximation
		3.10.8 Non-polynomial Interpolation
		3.10.9 Comparing Interpolation Operators
4 Reconstruction of the Degraded Image: Restoration
	4.1 Introduction
	4.2 Noise Model
		4.2.1 Gaussian Additive Noise
		4.2.2 Other Statistical Models of Noise
		4.2.3 Bipolar Impulse Noise
		4.2.4 Periodic and Multiplicative Noise
		4.2.5 Estimation of the Noise Parameters
	4.3 Spatial Filtering for Noise Removal
		4.3.1 Geometric Mean Filter
		4.3.2 Harmonic Mean Filter
		4.3.3 Contraharmonic Mean Filter
		4.3.4 Order-Statistics Filters
		4.3.5 Application of Spatial Mean Filters and on Order Statistics for Image Restoration
	4.4 Adaptive Filters
		4.4.1 Adaptive Median Filter
	4.5 Periodic Noise Reduction with Filtering in the Frequency Domain
		4.5.1 Notch Filters
		4.5.2 Optimum Notch Filtering
	4.6 Estimating the Degradation Function
		4.6.1 Derivation of HD by Observation of the Degraded Image
		4.6.2 Derivation of HD by Experimentation
		4.6.3 Derivation of HD by Physical–Mathematical Modeling: Motion Blurring
		4.6.4 Derivation of HD by Physical–Mathematical Modeling: Blurring by Atmospheric Turbulence
	4.7 Inverse Filtering—Deconvolution
		4.7.1 Application of the Inverse Filter: Example 1
		4.7.2 Application of the Inverse Filter: Example 2
		4.7.3 Application of the Inverse Filter: Example 3
	4.8 Optimal Filter
		4.8.1 Filtro di Wiener
		4.8.2 Analysis of the Wiener Filter
		4.8.3 Application of the Wiener Filter: One-Dimensional Case
		4.8.4 Application of the Wiener Filter: Two-Dimensional Case
	4.9 Power Spectrum Equalization—PSE Filter
	4.10 Constrained Least Squares Filtering
	4.11 Geometric Mean Filtering
	4.12 Nonlinear Iterative Deconvolution Filter
	4.13 Blind Deconvolution
	4.14 Nonlinear Diffusion Filter
	4.15 Bilateral Filter
	4.16 Dehazing
5 Image Segmentation
	5.1 Introduction
	5.2 Regions and Contours
	5.3 The Segmentation Process
		5.3.1 Segmentation by Global Threshold
	5.4 Segmentation Methods by Local Threshold
		5.4.1 Method Based on the Objects/Background Ratio
		5.4.2 Method Based on Histogram Analysis
		5.4.3 Method Based on the Gradient and Laplacian
		5.4.4 Method Based on Iterative Threshold Seclection
		5.4.5 Method Based on Inter-class Maximum Variance - Otsu
		5.4.6 Method Based on Adaptive Threshold
		5.4.7 Method Based on Multi-band Threshold for Color and Multi-spectral Images
	5.5 Segmentation Based on Contour Extraction
		5.5.1 Edge Following
		5.5.2 Connection of Broken Contour Sections
		5.5.3 Connected Components Labeling
		5.5.4 Filling Algorithm for Complex Regions
		5.5.5 Contour Extraction Using the Hough Transform
	5.6 Region Based Segmentation
		5.6.1 Region-Growing Segmentation
		5.6.2 Region-Splitting Segmentation
		5.6.3 Split-and-Merge Image Segmentation
	5.7 Segmentation by Watershed Transform
		5.7.1 Watershed Algorithm Based on Flooding Simulation
		5.7.2 Watershed Algorithm Using Markers
	5.8 Segmentation Using Clustering Algorithms
		5.8.1 Segmentation Using K-Means Algorithm
		5.8.2 Segmentation Using Mean-Shift Algorithm
6 Detectors and Descriptors of Interest Points
	6.1 Introduction
	6.2 Point of Interest Detector—Moravec
		6.2.1 Limitations of the Moravec Operator
	6.3 Point of Interest Detector—Harris–Stephens
		6.3.1 Limits and Properties of the Harris Algorithm
	6.4 Variations of the Harris–Stephens Algorithm
	6.5 Point of Interest Detector—Hessian
	6.6 Scale-Invariant Interest Points
		6.6.1 Scale-Space Representation
	6.7 Scale-Invariant Interest Point Detectors and Descriptors
		6.7.1 SIFT Detector and Descriptor
		6.7.2 SIFT Detector Component
		6.7.3 SIFT Descriptor Component
		6.7.4 GLOH Descriptor
	6.8 SURF Detector and Descriptor
		6.8.1 SURF Detector Component
		6.8.2 SURF Descriptor Component
		6.8.3 Harris–Laplace Detector
		6.8.4 Hessian–Laplace Detector
	6.9 Affine-Invariant Interest Point Detectors
		6.9.1 Harris-Affine Detector
		6.9.2 Hessian-Affine Detector
	6.10 Corner Fast Detectors
		6.10.1 SUSAN—Smallest Univalue Segment Assimilating Nucleus Detector
		6.10.2 Trajkovic–Hedley Segment Test Detector
		6.10.3 FAST—Features from Accelerated Segment Test Detector
	6.11 Regions Detectors and Descriptors
		6.11.1 MSER—Maximally Stable Extremal Regions Detector
		6.11.2 IBR—Intensity Extrema-Based Regions Detector
		6.11.3 Affine Salient Regions Detector
		6.11.4 EBR—Edge-Based Region Detector
		6.11.5 PCBR—Principal Curvature Based Region Detector
		6.11.6 SISF—Scale-Invariant Shape Features Detector
	6.12 Summary and Conclusions
Index