Inhaltsangabe
1 Introduction.- Summary of the Chapters.- Notation.- Teaching a Course from This Book.- The Problems.- Aspects of Imaging.- Computer Code.- Literature References.- Recommendation.- 2 The Image Plane.- Modes of Representation.- Some Properties of a Function of Two Variables.- Projection of Solid Objects.- Image Distortion.- Operations in the Image Plane.- Binary Images.- Operations on Digital Images.- Reflectance Distribution.- Data Compression.- Summary.- Appendix: A Contour Plot Programt.- Literature Cited.- Further Reading.- Problems.- 3 Two-Dimensional Impulse Functions.- The Two-Dimensional Point Impulse.- Rules for Interpreting Delta Notation.- Generalized Functions.- The Shah Functions iii and 2III.- Line Impulses.- Regular Impulse Patterns.- Interpretation of Rectangle Function of f(x).- Interpretation of Rectangle Function of f(x,y).- General Rule for Line Deltas.- The Ring Impulse.- Impulse Function of f(x,y).- Sifting Property.- Derivatives of Impulses.- Summary.- Literature Cited.- Problems.- 4 The Two-Dimensional Fourier Transform.- One Dimension.- The Fourier Component in Two Dimensions.- Three or More Dimensions.- Vector Form of Transform.- The Corrugation Viewpoint.- Examples of Transform Pairs.- Theorems for Two-Dimensional Fourier Transforms.- The Two-Dimensional Hartley Transform.- Theorems for the Hartley Transform.- Discrete Transforms.- Summary.- Literature Cited.- Further Reading.- Problems.- 5 Two-Dimensional Convolution.- Convolution Defined.- Cross-Correlation Defined.- Feature Detection by Matched Filtering.- Autocorrelation Defined.- Understanding Autocorrelation.- Cross-Correlation Islands and Dilation.- Lazy Pyramid and Chinese Hat Function.- Central Value and Volume of Autocorrelation.- The Convolution Sum.- Computing the Convolution.- Digital Smoothing.- Matrix Product Notation.- Summary.- Literature Cited.- Problems.- 6 The Two-Dimensional Convolution Theorem.- Convolution Theorem.- An Instrumental Caution.- Point Response and Transfer Function.- Autocorrelation Theorem.- Cross-Correlation Theorem.- Factorization and Separation.- Convolution with the Hartley Transform.- Summary.- Problems.- 7 Sampling and Interpolation in Two Dimensions.- What is a Sample?.- Sampling at a Point.- Sampling on a Point Pattern, and the Associated Transfer Function.- Sampling Along a Line.- Curvilinear Sampling.- The Shah Function.- Fourier Transform of the Shah Function.- Other Patterns of Sampling.- Factoring.- The Two-Dimensional Sampling Theorem.- Undersampling.- Aliasing.- Circular Cutoff.- Double-Rectangle Pass Band.- Discrete Aspect of Sampling.- Interpolating Between Samples.- Interlaced Sampling.- Appendix: The Two-Dimensional Fourier Transform of the Shah Function.- Literature Cited.- Problems.- 8 Digital Operations.- Smoothing.- Nonconvolutional Smoothing.- Trend Reduction.- Sharpening.- What is a Digital Filter?.- Guard Zone.- Transform Aspect of Smoothing Operator.- Finite Impulse Response (FIR).- Special Filters.- Densifying.- The Arbitrary Operator.- Derivatives.- The Laplacian Operator.- Projection as a Digital Operation.- Moire Patterns.- Functions of an Image.- Digital Representation of Objects.- Filling a Polygon.- Edge Detection and Segmentation.- Discrete Binary Objects.- Operations on Discrete Binary Objects.- Union and Intersection.- Pixel Morphology.- Dilation.- Coding a Binary Matrix.- Granulometry.- Conclusion.- Literature Cited.- Problems.- 9 Rotational Symmetry.- What Is a Bessel Function?.- The Hankel Transform.- The jinc Function.- The Struve Function.- The Abel Transform.- Spin Averaging.- Angular Variation and Chebyshev Polynomials.- Summary.- Table of the jinc Function.- Problems.- 10 Imaging by Convolution.- Mapping by Antenna Beam.- Scanning the Spherical Sky.- Photography.- Microdensitometry.- Video Recording.- Eclipsometry.- The Scanning Acoustic Microscope.- Focusing Underwater Sound.- Literature Cited.- Problems.- 11 Diffraction Theory of Sensors and Radiators.- The Concept of
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