Digital picture processing : an introduction

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.