Digital Picture Processing : An Introduction

The text has been prepared for researchers involved in picture processing. It is designed to help them in mastering the methods at the professional level. From the viewpoint of both signal theory and information theory, the treatment covers the basic principles of the digital methods for the processing of continuous signals such as picture signals. In addition, it reviews schemes for correcting signal distortion in imaging systems, for the enhancement of picture contrast, and for the automatic measurement of picture details. The text contains new results on digital filtering and transformation, and a new approach to picture processing. The main applications, as documented by numerous examples, are in space research, remote sensing, medical diag­ nostics, nondestructive testing. The material has been tested extensively in class-room use with students of both computer science and electrical engineering at the senior undergraduate and the first-year graduate level. The present edition is not a translation of the original Russian book, but it has been extended substantially as well as updated. The author is grate­ ful to Dr. H. Lotsch of Springer-Verlag for his proposal to prepare this text and for many helpful suggestions. He likes to thank Dr. P. Hawkes for a careful copy-editing of the manuscript, and acknowledges numerous criti­ cal comments by Professors S.L. Gorelik, T.S. Huang, A.W. Lohmann,and A.M. Trakhtman.

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.