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Dedication
by Eric Dubois
Multidimensional Signal and Color Image Processing Using Lattices
Cover
Dedication
About the Companion Website
1 Introduction
2 Continuous‐Domain Signals and Systems
2.1 Introduction
2.2 Multidimensional Signals
2.3 Visualization of Two‐Dimensional Signals
2.4 Signal Spaces and Systems
2.5 Continuous‐Domain Linear Systems
2.6 The Multidimensional Fourier Transform
2.7 Further Properties of Differentiation and Related Systems
3 Discrete‐Domain Signals and Systems
3.1 Introduction
3.2 Lattices
3.3 Sampling Structures
3.4 Signals Defined on Lattices
3.5 Special Multidimensional Signals on a Lattice
3.6 Linear Systems Over Lattices
3.7 Discrete‐Domain Fourier Transforms Over a Lattice
3.8 Finite Impulse Response (FIR) Filters
4 Discrete‐Domain Periodic Signals
4.1 Introduction
4.2 Periodic Signals
4.3 Linear Shift‐Invariant Systems
4.4 Discrete‐Domain Periodic Fourier Transform
4.5 Properties of the Discrete‐Domain Periodic Fourier Transform
4.6 Computation of the Discrete‐Domain Periodic Fourier Transform
4.7 Vector Space Representation of Images Based on the Discrete‐Domain Periodic Fourier Transform
5 Continuous‐Domain Periodic Signals
5.1 Introduction
5.2 Continuous‐Domain Periodic Signals
5.3 Linear Shift‐Invariant Systems
5.4 Continuous‐Domain Periodic Fourier Transform
5.5 Properties of the Continuous‐Domain Periodic Fourier Transform
5.6 Evaluation of the Continuous‐Domain Periodic Fourier Transform
6 Sampling, Reconstruction and Sampling Theorems for Multidimensional Signals
6.1 Introduction
6.2 Ideal Sampling and Reconstruction of Continuous‐Domain Signals
6.3 Practical Sampling
6.4 Practical Reconstruction
6.5 Sampling and Periodization of Multidimensional Signals and Transforms
6.6 Inverse Fourier Transforms
6.7 Signals and Transforms with Finite Support
7 Light and Color Representation in Imaging Systems
7.1 Introduction
7.2 Light
7.3 The Space of Light Stimuli
7.4 The Color Vector Space
7.5 Color Coordinate Systems
8 Processing of Color Signals
8.1 Introduction
8.2 Continuous‐Domain Systems for Color Images
8.3 Discrete‐Domain Color Images
8.4 Color Mosaic Displays
9 Random Field Models
9.1 Introduction
9.2 What is a Random Field?
9.3 Image Moments
9.4 Power Density Spectrum
9.5 Filtering and Sampling of WSS Random Fields
9.6 Estimation of the Spectral Density Matrix
10 Analysis and Design of Multidimensional FIR Filters
10.1 Introduction
10.2 Moving Average Filters
10.3 Gaussian Filters
10.4 Band‐pass and Band‐stop Filters
10.5 Frequency‐Domain Design of Multidimensional FIR Filters
11 Changing the Sampling Structure of an Image
11.1 Introduction
11.2 Sublattices
11.3 Upsampling
11.4 Downsampling
11.5 Arbitrary Sampling Structure Conversion
12 Symmetry Invariant Signals and Systems
12.1 LSI Systems Invariant to a Group of Symmetries
12.2 Symmetry‐Invariant Discrete‐Domain Periodic Signals and Systems
12.3 Vector‐Space Representation of Images Based on the Symmetry‐Invariant Periodic Fourier Transform
13 Lattices
13.1 Introduction
13.2 Basic Definitions
13.3 Properties of Lattices
13.4 Reciprocal Lattice
13.5 Sublattices
13.6 Cosets and the Quotient Group
13.7 Basis Transformations
13.8 Smith Normal Form
13.9 Intersection and Sum of Lattices
Appendix A Equivalence Relations
Appendix B Groups
Appendix C Vector Spaces
Appendix D Multidimensional Fourier Transform Properties
References
Index
End User License Agreement
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