Mathematics of Digital Images: Creation, Compression, Restoration, Recognition free download online
Title: Mathematics of Digital Images: Creation, Compression, Restoration, Recognition Author(s): S. G. Hoggar Pages: 854 Publisher: Cambridge University Press Publication date: 2006 Language: English Format: PDF ISBN-10: 0521780292 ISBN-13: Description: This major revision of the author's popular book still focuses on foundations and proofs, but now exhibits a shift away from Topology to Probability and Information Theory (with Shannon's source and channel encoding theorems) which are used throughout. Three vital areas for the digital revolution are tackled (compression, restoration and recognition), establishing not only what is true, but why, to facilitate education and research. It will remain a valuable book for computer scientists, engineers and applied mathematicians.
Review
"Recognition explains the mathematics needed to carry out various aspects of digital imaging through examples, exercises with solutions, pseudocode and sample calculations on images. Suitable for a course or tutorial."
Spectra
"This book explains the mathematics needed to understand and carry out these components in a style at once rigorous and practical, with many worked examples, exercises and solutions, pseudocode, and sample calculations on images."
Bookshelf
"This book covers a lot of ground!"
Jason Dowling, IAPR Newsletter
"...offers both theory and practical applications and exercises. College-level courses will want to consider this as a classroom text on the subject, but specialty libraries will also find it a popular pick for advanced self-study." - California Bookwatch Diane C. Donovan, Midwest Book Review
Contents
Preface
Introduction
A word on notation
List of symbols
Part I The plane
1 Isometries
1.1 Introduction
1.2 Isometries and their sense
1.3 The classification of isometries
Exercises 1
2 How isometries combine
2.1 Reflections are the key
2.2 Some useful compositions
2.3 The image of a line of symmetry
2.4 The dihedral group
2.5 Appendix on groups
Exercises 2
3 The seven braid patterns
Constructing braid patterns
Exercises 3
4 Plane patterns and symmetries
4.1 Translations and nets
4.2 Cells
4.3 The five net types
Exercises 4
5 The 17 plane patterns
5.1 Preliminaries
5.2 The general parallelogram net
5.3 The rectangular net
5.4 The centred rectangular net
5.5 The square net
5.6 The hexagonal net
5.7 Examples of the 17 plane pattern types
5.8 Scheme for identifying pattern types
Exercises 5
6 More plane truth
6.1 Equivalent symmetry groups
6.2 Plane patterns classified
6.3 Tilings and Coxeter graphs
6.4 Creating plane patterns
Exercises 6
Part II Matrix structures
7 Vectors and matrices
7.1 Vectors and handedness
7.2 Matrices and determinants
7.3 Further products of vectors in 3-space
7.4 The matrix of a transformation
7.5 Permutations and the proof of Determinant Rules
Exercises 7
8 Matrix algebra
8.1 Introduction to eigenvalues
8.2 Rank, and some ramifications
8.3 Similarity to a diagonal matrix
8.4 The Singular Value Decomposition (SVD)
Exercises 8
Part III Here's to probability
9 Probability
9.1 Sample spaces
9.2 Bayes' Theorem
9.3 Random variables
9.4 A census of distributions
9.5 Mean inequalities
Exercises 9
10 Random vectors
10.1 Random vectors
10.2 Functions of a random vector
10.3 The ubiquity of normal/Gaussian variables
10.4 Correlation and its elimination
Exercises 10
11 Sampling and inference
11.1 Statistical inference
11.2 The Bayesian approach
11.3 Simulation
11.4 Markov Chain Monte Carlo
Exercises 11
Part IV Information, error and belief
12 Entropy and coding
12.1 The idea of entropy
12.2 Codes and binary trees
12.3 Huffman text compression
12.4 The redundancy of Huffman codes
12.5 Arithmetic codes
12.6 Prediction by Partial Matching
12.7 LZW compression
12.8 Entropy and Minimum Description Length (MDL)
Exercises 12
13 Information and error correction
13.1 Channel capacity
13.2 Error-correcting codes
13.3 Probabilistic decoding
13.4 Postscript: Bayesian nets in computer vision
Exercises 13
PartV Transforming the image
14 The Fourier Transform
14.1 The Discrete Fourier Transform
14.2 The Continuous Fourier Transform
14.3 DFT connections
Exer
Mathematics of Digital Images: Creation, Compression, Restoration, Recognition free download links:
Title: Mathematics of Digital Images: Creation, Compression, Restoration, Recognition