Muutke küpsiste eelistusi

Image Processing Tour of College Mathematics [Kõva köide]

Teised raamatud teemal:
Image Processing Tour of College MathematicsSuurem pilt
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367002022.html
Märksõnad:
An Image Processing Tour of College Mathematics aims to provide meaningful context for reviewing key topics of the college mathematics curriculum, to help students gain confidence in using concepts and techniques of applied mathematics, to increase student awareness of recent developments in mathematical sciences, and to help students prepare for graduate studies.

The topics covered include a library of elementary functions, basic concepts of descriptive statistics, probability distributions of functions of random variables, definitions and concepts behind first- and second-order derivatives, most concepts and techniques of traditional linear algebra courses, an introduction to Fourier analysis, and a variety of discrete wavelet transforms all of that in the context of digital image processing.

Features











Pre-calculus material and basic concepts of descriptive statistics are reviewed in the context of image processing in the spatial domain.





Key concepts of linear algebra are reviewed both in the context of fundamental operations with digital images and in the more advanced context of discrete wavelet transforms.





Some of the key concepts of probability theory are reviewed in the context of image equalization and histogram matching.





The convolution operation is introduced painlessly and naturally in the context of naïve filtering for denoising and is subsequently used for edge detection and image restoration.





An accessible elementary introduction to Fourier analysis is provided in the context of image restoration.





Discrete wavelet transforms are introduced in the context of image compression, and the readers become more aware of some of the recent developments in applied mathematics.





This text helps students of mathematics ease their way into mastering the basics of scientific computer programming.

Arvustused

"Each chapter includes a mixture of theoretical exercises and computational exercises to be done using MATLAB. [ . . .] This textbook should be of interest to instructors who want to teach an introductory course on the mathematics Fourier and wavelet transform methods for image processing at the advanced undergraduate level." Mathematical Association of America

Preface ix
1 Introduction to Basics of Digital Images
1(20)
1.1 Grayscale Digital Images
1(2)
1.2 Working with Images in MATLAB®
3(4)
1.3 Images and Statistical Description of Quantitative Data
7(9)
1.3.1 Image Histograms
7(3)
1.3.2 Measures of Center and Spread
10(6)
1.4 Color Images and Color Spaces
16(5)
2 A Library of Elementary Functions
21(34)
2.1 Introduction
21(1)
2.2 Power Functions and Gamma-Correction
22(8)
2.3 Exponential Functions and Image Transformations
30(5)
2.4 Logarithmic Functions and Image Transformations
35(6)
2.5 Linear Functions and Contrast Stretching
41(9)
2.6 Automation of Image Enhancement
50(5)
3 Probability, Random Variables, and Histogram Processing
55(20)
3.1 Introduction
55(1)
3.2 Discrete and Continuous Random Variables
56(7)
3.3 Transformation of Random Variables
63(6)
3.4 Image Equalization and Histogram Matching
69(6)
4 Matrices and Linear Transformations
75(28)
4.1 Basic Operations on Matrices
75(10)
4.2 Linear Transformations and Their Matrices
85(11)
4.3 Homogeneous Coordinates and Projective Transformations
96(7)
5 Convolution and Image Filtering
103(48)
5.1 Image Blurring and Noise Reduction
103(9)
5.2 Convolution: Definitions and Examples
112(20)
5.2.1 Discrete Linear Convolution
113(5)
5.2.2 Circular Convolution
118(3)
5.2.3 Algebraic Properties of Convolution
121(1)
5.2.4 Convolution as a Linear Transformation
122(2)
5.2.5 Convolution in Two Dimensions
124(8)
5.3 Edge Detection
132(18)
5.3.1 Partial Derivatives and the Gradient Edge Detector
133(3)
5.3.2 Directional Derivatives and the Roberts Cross Operator
136(1)
5.3.3 The Prewitt and Sobel Edge Detectors
137(3)
5.3.4 Laplacian Edge Detection
140(3)
5.3.5 Edge Detection in Noisy Images
143(2)
5.3.6 Boolean Convolution and Edge Dilation
145(5)
5.4
Chapter Summary
150(1)
6 Analysis and Processing in the Frequency Domain
151(108)
6.1 Introduction
151(2)
6.2 Frequency Analysis of Continuous Periodic Signals
153(43)
6.2.1 Trigonometric Fourier Coefficients of 1-Periodic Signals
154(15)
6.2.2 A Refresher on Complex Numbers
169(7)
6.2.3 Complex Fourier Coefficients
176(6)
6.2.4 Properties of Fourier Coefficients
182(7)
6.2.5 T-Periodic Signals
189(7)
6.3 Inner Products, Orthogonal Bases, and Fourier Coefficients
196(12)
6.4 Discrete Fourier Transform
208(34)
6.4.1 Discrete Periodic Sequences
208(7)
6.4.2 DFT: Definition, Examples, and Basic Properties
215(16)
6.4.3 Placing the DFT on a Firm Foundation
231(3)
6.4.4 Linear Time-Invariant Transformations and the DFT
234(8)
6.5 Discrete Fourier Transform in 2D
242(15)
6.5.1 Definition, Examples, and Properties
242(3)
6.5.2 Frequency Domain Processing of Digital Images
245(12)
6.6
Chapter Summary
257(2)
7 Wavelet-Based Methods in Image Compression
259(70)
7.1 Introduction
259(1)
7.2 Naive Compression in One Dimension
260(3)
7.3 Entropy and Entropy Encoding
263(4)
7.4 The Discrete Haar Wavelet Transform
267(5)
7.5 Haar Wavelet Transforms of Digital Images
272(9)
7.6 Discrete-Time Fourier Transform
281(5)
7.7 From the Haar Transform to Daubechies Transforms
286(11)
7.8 Biorthogonal Wavelet Transforms
297(19)
7.8.1 Biorthogonal Spline Filters
300(9)
7.8.2 Daubechies Theorem for Biorthogonal Spline Filters
309(2)
7.8.3 The CDF97 Transform
311(5)
7.9 An Overview of JPEG2000
316(2)
7.10 Other Applications of Wavelet Transforms
318(11)
7.10.1 Wavelet-Based Edge Detection
318(3)
7.10.2 Wavelet-Based Image Denoising
321(8)
Bibliography 329(4)
Index 333
Yevgeniy V. Galperin is Associate Professor of Mathematics at East Stroudsburg University of Pennsylvania. He holds a PhD in mathematics and has published several papers in the field of time-frequency analysis and related areas of Fourier analysis. His research and academic interests also include numerical methods, simulation of stochastic processes for real-life applications, and mathematical pedagogy. He has given numerous conference presentations on instructional and course-design approaches directed at increasing student motivation and awareness of societal value of mathematics and on incorporating signal and image processing into the undergraduate mathematics curriculum.