Digital Picture Processing

1. Introduction.- 1 Fundamentals of the Theory of Digital Signal Processing.- 2. Elements of Signal Theory.- 2.1 Signals as Mathematical Functions.- 2.2 Signal Space.- 2.3 The Most Common Systems of Basis Functions.- 2.3.1 Impulse Basis Functions.- 2.3.2 Harmonic Functions.- 2.3.3 Walsh Functions.- 2.3.4 Haar Functions.- 2.3.5 Sampling Functions.- 2.4 Continuous Representations of Signals.- 2.5 Description of Signal Transformations.- 2.5.1 Linear Transformations.- 2.5.2 Nonlinear Element-by-Element Transforms.- 2.6 Representation of Linear Transformations with Respect to Discrete Bases.- 2.6.1 Representation Using Vector Responses.- 2.6.2 Matrix Representations.- 2.6.3 Representation of Operators by Means of Their Eigenfunctions and Eigenvalues.- 2.7 Representing Operator with Respect to Continuous Bases.- 2.7.1 Operator Kernel.- 2.7.2 Description in Terms of Impulse Responses.- 2.7.3 Description Using Frequency Transfer Functions.- 2.7.4 Description with Input and Output Signals Referred to Different Bases.- 2.7.5 Description Using Eigenfunctions.- 2.8 Examples of Linear Operators.- 2.8.1 Shift-Invariant Filters.- 2.8.2 The Identity Operator.- 2.8.3 Shi ft Operator.- 2.8.4 Sampling Oparator.- 2.8.5 Gating Operator (Multiplier).- 3. Discretization and Quantization of Signals.- 3.1 Generalized Quantization.- 3.2 Concepts of Discretization and Element-by-Element Quantization.- 3.2.1 Discretization.- 3.2.2 Element-by-Element Quantization.- 3.3 The Sampling Theorem.- 3.4 Sampling Theory for Two-Dimensional Signals.- 3.5 Errors of Discretization and Restoration of Signals in Sampling Theory.- 3.6 Other Approaches to Discretization.- 3.7 Optimal Discrete Representation and Dimensionality of Signals.- 3.8 Element-by-Element Quantization.- 3.9 Examples of Optimum Quantization.- 3.9.1 Example: The Threshold Metric.- 3.9.2 Example: Power Criteria for the Absolute Value of the Quantization Error.- 3.9.3 Example: Power Criteria for the Relative Quantization Error.- 3.10 Quantization in the Presence of Noise. Quantization and Representation of Numbers in Digital Processors.- 3.11 Review of Picture-Coding Methods.- 4. Discrete Representations of Linear Transforms.- 4.1 Problem Formulation and General Approach.- 4.2 Discrete Representation of Shift-Invariant Filters for Band-Limited Signals.- 4.3 Digital Filters.- 4.4 Transfer Functions and Impulse Responses of Digital Filters.- 4.5 Boundary Effects in Digital Filtering.- 4.6 The Discrete Fourier Transform (DFT).- 4.7 Shifted, Odd and Even DFTs.- 4.8 Using Discrete Fourier Transforms.- 4.8.1 Calculating Convolutions.- 4.8.2 Signal Interpolation.- 4.9 Walsh and Similar Transforms.- 4.10 The Haar Tansform. Addition Elements of Matrix Calculus.- 4.11 Other Orthogonal Tansforms. General Representations. Review of Applications.- 5. Linear Transform Algorithms.- 5.1 Fast Algorithms of Discrete Orthogonal Transforms.- 5.2 Fast Haar Transform (FHT) Algorithms.- 5.3 Fast Walsh Transform (FWT) Algorithms.- 5.4 Fast Discrete Fourier Transform (FFT) Algorithms.- 5.5 Review of Other Fast Algorithms. Features of Two-Dimensional Transforms.- 5.5.1 Truncated FFT and FWT Algorithms.- 5.5.2 Transition Matrices Between Various Transforms.- 5.5.3 Calculation of Two-Dimensional Transforms.- 5.6 Combined DFT Algorithms.- 5.6.1 Combined DFT Algorithms of Real Sequences.- 5.6.2 Combined SDFT (1/2, 0) Algorithms of Even and Real Even Sequences.- 5.7 Recursive DFT Algorithms.- 5.8 Fast Algorithms for Calculating the DFT and Signal Convolution with Decreased Multiplication.- 6. Digital Statistical Methods.- 6.1 Principles of the Statistical Description of Pictures.- 6.2 Measuring the Grey-Level Distribution.- 6.2.1 Step Smoothing.- 6.2.2 Smoothing by Sliding Summation.- 6.2.3 Smoothing with Orthogonal Transforms.- 6.3 The Estimation of Correlation Functions and Spectra.- 6.3.1 Averaging Local Spectra.- 6.3.2 Masking (Windowing) the Process by Smooth Functions.- 6.3.3 Direct Smoothing of Spectra.- 6.4 Generating Pseudorandom Numbers.- 6.5 Measuring Picture Noise.- 6.5.1 The Prediction Method.- 6.5.2 The Voting Method.- 6.5.3 Measuring the Variance and the Auto-Correlation Function of Additive Wideband Noise.- 6.5.4 Evaluation of the Intensity and Frequency of the Harmonic Components of Periodic Interference and Other Types of Interference with Narrow Spectra.- 6.5.5 Evaluation of the Parameters of Pulse Noise, Quantization Noise and Strip-Like Noise.- 2 Picture Processing.- 7. Correcting Imaging Systems.- 7.1 Problem Formulation.- 7.2 Suppression of Additive Noise by Linear Filtering.- 7.3 Filtering of Pulse Interference.- 7.4 Correction of Linear Distortion.- 7.5 Correction of Amplitude Characteristics.- 8. Picture Enhancement and Preparation.- 8.1 Preparation Problems and Visual Analysis of Pictures.- 8.1.1 Feature Processing.- 8.1.2 Geometric Transformations.- 8.2 Adaptive Quantization of Modes.- 8.3 Preparation by Nonlinear Transformation of the Video Signal Scale.- 8.4 Linear Preparation Methods.- 8.5 Methods of Constructing Graphical Representation: Computer Graphics.- 8.6 Geometric Picture Transformation.- 8.6.1 Bilinear Interpolation.- 8.6.2 Interpolation Using DFT and SDFT.- 9. Measuring the Coordinates of Objects in Pictures.- 9.1 Problem Formulation.- 9.2 Localizing a Precisely Known Object in a Spatially Homogeneous Picture.- 9.3 Uncertainty in the Object and Picture Inhomogeneity. Localization in "Blurred" Pictures.- 9.3.1 "Exhaustive" Estimator.- 9.3.2 Estimator Seeking an Averaged Object.- 9.3.3 Adjustable Estimator with Fragment-by Fraament Optimal Fi1tering.- 9.3.4 Non-Adjustable Estimator.- 9.3.5 Localization in Blurred and Noisy Pictures.- 9.4 Optimal Localization and Picture Contours. Choice of Reference Objects.- 9.5 Algorithm for the Automatic Detection and Extraction of Bench-Marks in Aerial and Space Photographs.- 10-Conclusion.- References.