Mathematics of digital images: creation, compression, restoration, recognition
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2006
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXXII, 854 S. Ill., graph. Darst. |
| ISBN: | 0521780292 9780521780292 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface page xi
Introduction xiii
A word on notation xxvii
List of symbols xxix
Part I The plane 1
1 Isometries 3
1.1 Introduction 3
1.2 Isometries and their sense 6
1.3 The classification of isometries 16
Exercises 1 21
2 How isometries combine 23
2.1 Reflections are the key 24
2.2 Some useful compositions 25
2.3 The image of a line of symmetry 31
2.4 The dihedral group 36
2.5 Appendix on groups 40
Exercises 2 41
3 The seven braid patterns 43
Constructing braid patterns 45
Exercises 3 46
4 Plane patterns and symmetries 48
4.1 Translations and nets 48
4.2 Cells 50
4.3 The five net types 56
Exercises 4 63
5 The 17 plane patterns 64
5.1 Preliminaries 64
5.2 The general parallelogram net 66
5.3 The rectangular net 67
5.4 The centred rectangular net 68
viii Contents
5.5 The square net 69
5.6 The hexagonal net 71
5.7 Examples of the 17 plane pattern types 73
5.8 Scheme for identifying pattern types 75
Exercises 5 77
6 More plane truth 79
6.1 Equivalent symmetry groups 79
6.2 Plane patterns classified 82
6.3 Tilings and Coxeter graphs 91
6.4 Creating plane patterns 99
Exercises 6 109
Part II Matrix structures 113
7 Vectors and matrices 115
7.1 Vectors and handedness 115
7.2 Matrices and determinants 126
7.3 Further products of vectors in 3 space 140
7.4 The matrix of a transformation 145
7.5 Permutations and the proof of Determinant Rules 155
Exercises 7 159
8 Matrix algebra 162
8.1 Introduction to eigenvalues 162
8.2 Rank, and some ramifications 172
8.3 Similarity to a diagonal matrix 180
8.4 The Singular Value Decomposition (SVD) 192
Exercises 8 203
Part III Here s to probability 207
9 Probability 209
9.1 Sample spaces 209
9.2 Bayes Theorem 217
9.3 Random variables 227
9.4 A census of distributions 239
9.5 Mean inequalities 251
Exercises 9 256
10 Random vectors 258
10.1 Random vectors 258
10.2 Functions of a random vector 265
10.3 The ubiquity of normal/Gaussian variables 277
10.4 Correlation and its elimination 285
Exercises 10 302
11 Sampling and inference 303
11.1 Statistical inference 304
11.2 The Bayesian approach 324
Contents ix
11.3 Simulation 335
11.4 Markov Chain Monte Carlo 344
Exercises 11 389
Part IV Information, error and belief 393
12 Entropy and coding 395
12.1 The idea of entropy 395
12.2 Codes and binary trees 402
12.3 Huffman text compression 406
12.4 The redundancy of Huffman codes 412
12.5 Arithmetic codes 417
12.6 Prediction by Partial Matching 424
12.7 LZW compression 425
12.8 Entropy and Minimum Description Length (MDL) 429
Exercises 12 442
13 Information and error correction 444
13.1 Channel capacity 444
13.2 Error correcting codes 469
13.3 Probabilistic decoding 493
13.4 Postscript: Bayesian nets in computer vision 516
Exercises 13 518
Part V Transforming the image 521
14 The Fourier Transform 523
14.1 The Discrete Fourier Transform 523
14.2 The Continuous Fourier Transform 540
14.3 DFT connections 546
Exercises 14 558
15 Transforming images 560
15.1 The Fourier Transform in two dimensions 5 61
15.2 Filters 578
15.3 Deconvolution and image restoration 595
15.4 Compression 617
15.5 Appendix 628
Exercises 15 635
16 Scaling 637
16.1 Nature, fractals and compression 637
16.2 Wavelets 658
16.3 The Discrete Wavelet Transform 665
16.4 Wavelet relatives 677
Exercises 16 683
x Contents
Part VI See, edit, reconstruct 685
17 B spline wavelets 687
17.1 Splines from boxes 687
17.2 The step to subdivision 703
17.3 The wavelet formulation 719
17.4 Appendix: band matrices for finding Q, A and B 732
17.5 Appendix: surface wavelets 743
Exercises 17 754
18 Further methods 757
18.1 Neural networks 757
18.2 Self organising nets 783
18.3 Information Theory revisited 792
18.4 Tomography 818
Exercises 18 830
References 832
Index 845
|
| adam_txt |
Contents
Preface page xi
Introduction xiii
A word on notation xxvii
List of symbols xxix
Part I The plane 1
1 Isometries 3
1.1 Introduction 3
1.2 Isometries and their sense 6
1.3 The classification of isometries 16
Exercises 1 21
2 How isometries combine 23
2.1 Reflections are the key 24
2.2 Some useful compositions 25
2.3 The image of a line of symmetry 31
2.4 The dihedral group 36
2.5 Appendix on groups 40
Exercises 2 41
3 The seven braid patterns 43
Constructing braid patterns 45
Exercises 3 46
4 Plane patterns and symmetries 48
4.1 Translations and nets 48
4.2 Cells 50
4.3 The five net types 56
Exercises 4 63
5 The 17 plane patterns 64
5.1 Preliminaries 64
5.2 The general parallelogram net 66
5.3 The rectangular net 67
5.4 The centred rectangular net 68
viii Contents
5.5 The square net 69
5.6 The hexagonal net 71
5.7 Examples of the 17 plane pattern types 73
5.8 Scheme for identifying pattern types 75
Exercises 5 77
6 More plane truth 79
6.1 Equivalent symmetry groups 79
6.2 Plane patterns classified 82
6.3 Tilings and Coxeter graphs 91
6.4 Creating plane patterns 99
Exercises 6 109
Part II Matrix structures 113
7 Vectors and matrices 115
7.1 Vectors and handedness 115
7.2 Matrices and determinants 126
7.3 Further products of vectors in 3 space 140
7.4 The matrix of a transformation 145
7.5 Permutations and the proof of Determinant Rules 155
Exercises 7 159
8 Matrix algebra 162
8.1 Introduction to eigenvalues 162
8.2 Rank, and some ramifications 172
8.3 Similarity to a diagonal matrix 180
8.4 The Singular Value Decomposition (SVD) 192
Exercises 8 203
Part III Here's to probability 207
9 Probability 209
9.1 Sample spaces 209
9.2 Bayes' Theorem 217
9.3 Random variables 227
9.4 A census of distributions 239
9.5 Mean inequalities 251
Exercises 9 256
10 Random vectors 258
10.1 Random vectors 258
10.2 Functions of a random vector 265
10.3 The ubiquity of normal/Gaussian variables 277
10.4 Correlation and its elimination 285
Exercises 10 302
11 Sampling and inference 303
11.1 Statistical inference 304
11.2 The Bayesian approach 324
Contents ix
11.3 Simulation 335
11.4 Markov Chain Monte Carlo 344
Exercises 11 389
Part IV Information, error and belief 393
12 Entropy and coding 395
12.1 The idea of entropy 395
12.2 Codes and binary trees 402
12.3 Huffman text compression 406
12.4 The redundancy of Huffman codes 412
12.5 Arithmetic codes 417
12.6 Prediction by Partial Matching 424
12.7 LZW compression 425
12.8 Entropy and Minimum Description Length (MDL) 429
Exercises 12 442
13 Information and error correction 444
13.1 Channel capacity 444
13.2 Error correcting codes 469
13.3 Probabilistic decoding 493
13.4 Postscript: Bayesian nets in computer vision 516
Exercises 13 518
Part V Transforming the image 521
14 The Fourier Transform 523
14.1 The Discrete Fourier Transform 523
14.2 The Continuous Fourier Transform 540
14.3 DFT connections 546
Exercises 14 558
15 Transforming images 560
15.1 The Fourier Transform in two dimensions 5 61
15.2 Filters 578
15.3 Deconvolution and image restoration 595
15.4 Compression 617
15.5 Appendix 628
Exercises 15 635
16 Scaling 637
16.1 Nature, fractals and compression 637
16.2 Wavelets 658
16.3 The Discrete Wavelet Transform 665
16.4 Wavelet relatives 677
Exercises 16 683
x Contents
Part VI See, edit, reconstruct 685
17 B spline wavelets 687
17.1 Splines from boxes 687
17.2 The step to subdivision 703
17.3 The wavelet formulation 719
17.4 Appendix: band matrices for finding Q, A and B 732
17.5 Appendix: surface wavelets 743
Exercises 17 754
18 Further methods 757
18.1 Neural networks 757
18.2 Self organising nets 783
18.3 Information Theory revisited 792
18.4 Tomography 818
Exercises 18 830
References 832
Index 845 |
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| spelling | Hoggar, Stuart G. Verfasser aut Mathematics of digital images creation, compression, restoration, recognition S. G. Hoggar 1. publ. Cambridge Cambridge Univ. Press 2006 XXXII, 854 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bildverarbeitung - Mathematik Mathematik Image processing Digital techniques Mathematics Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Computergrafik (DE-588)4010450-3 gnd rswk-swf Computergrafik (DE-588)4010450-3 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Bildverarbeitung (DE-588)4006684-8 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014742337&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hoggar, Stuart G. Mathematics of digital images creation, compression, restoration, recognition Bildverarbeitung - Mathematik Mathematik Image processing Digital techniques Mathematics Bildverarbeitung (DE-588)4006684-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd Computergrafik (DE-588)4010450-3 gnd |
| subject_GND | (DE-588)4006684-8 (DE-588)4114528-8 (DE-588)4010450-3 |
| title | Mathematics of digital images creation, compression, restoration, recognition |
| title_auth | Mathematics of digital images creation, compression, restoration, recognition |
| title_exact_search | Mathematics of digital images creation, compression, restoration, recognition |
| title_exact_search_txtP | Mathematics of digital images creation, compression, restoration, recognition |
| title_full | Mathematics of digital images creation, compression, restoration, recognition S. G. Hoggar |
| title_fullStr | Mathematics of digital images creation, compression, restoration, recognition S. G. Hoggar |
| title_full_unstemmed | Mathematics of digital images creation, compression, restoration, recognition S. G. Hoggar |
| title_short | Mathematics of digital images |
| title_sort | mathematics of digital images creation compression restoration recognition |
| title_sub | creation, compression, restoration, recognition |
| topic | Bildverarbeitung - Mathematik Mathematik Image processing Digital techniques Mathematics Bildverarbeitung (DE-588)4006684-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd Computergrafik (DE-588)4010450-3 gnd |
| topic_facet | Bildverarbeitung - Mathematik Mathematik Image processing Digital techniques Mathematics Bildverarbeitung Mathematisches Modell Computergrafik |
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