Presents recent significant and rapid development in the field of 2D and 3D image analysis

2D and 3D Image Analysis by Moments, is a unique compendium of moment-based image analysis which includes traditional methods and also reflects the latest development of the field.

The book presents a survey of 2D and 3D moment invariants with respect to similarity and affine spatial transformations and to image blurring and smoothing by various filters. The book comprehensively describes the mathematical background and theorems about the invariants but a large part is also devoted to practical usage of moments. Applications from various fields of computer vision, remote sensing, medical imaging, image retrieval, watermarking, and forensic analysis are demonstrated. Attention is also paid to efficient algorithms of moment computation.

Key features:

• Presents a systematic overview of moment-based features used in 2D and 3D image analysis.
• Demonstrates invariant properties of moments with respect to various spatial and intensity transformations.
• Reviews and compares several orthogonal polynomials and respective moments.
• Describes efficient numerical algorithms for moment computation.
• It is a "classroom ready" textbook with a self-contained introduction to classifier design.
• The accompanying website contains around 300 lecture slides, Matlab codes, complete lists of the invariants, test images, and other supplementary material.

2D and 3D Image Analysis by Moments, is ideal for mathematicians, computer scientists, engineers, software developers, and Ph.D students involved in image analysis and recognition. Due to the addition of two introductory chapters on classifier design, the book may also serve as a self-contained textbook for graduate university courses on object recognition.

Jan Flusser is a professor of Computer Science and a director of the Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic. His research interest covers moments and moment invariants, image registration, image fusion, multichannel blind deconvolution, and super-resolution imaging. He has authored and coauthored more than 200 research publications, including the monograph Moments and Moment Invariants in Pattern Recognition (Wiley, 2009), and has delivered 20 tutorials and invited/keynote talks at major conferences. His publications have received about 10,000 citations. Jan Flusser received several scientific awards and prizes, such as the Award of the Chairman of the Czech Science Foundation (2007), the Prize of the Czech Academy of Sciences (2007), the SCOPUS 1000 Award presented by Elsevier (2010), and the Felber Medal of the Czech Technical University for excellent contribution to research and education (2015).

TomáS Suk received a Ph.D degree in computer science from the Czechoslovak Academy of Sciences in 1992. He is a senior research fellow with the Institute of Information Theory and Automation, Czech Academy of Sciences, Prague. His research interests include invariant features, moment and point-based invariants, color spaces, geometric transformations, and applications in botany, remote sensing, astronomy, medicine, and computer vision. He has authored and coauthored more than 30 journal papers and 50 conference papers in these areas, including tutorials on moment invariants held at the conferences ICIP'07 and SPPRA'09. He coauthored the monograph Moments and Moment Invariants in Pattern Recognition (Wiley, 2009). His publications have received about 1000 citations. In 2002 he received the Otto Wichterle Premium of the Czech Academy of Sciences for young scientists.

Barbara Zitová received her Ph.D degree in software systems from the Charles University, Prague, Czech Republic, in 2000. She is a head of Department of Image Processing at the Institute of Information Theory and Automation, Czech Academy of Sciences, Prague. She teaches courses on Digital Image Processing and Wavelets in Image Processing. Her research interests include geometric invariants, image enhancement, image registration, image fusion, medical image processing, and applications in cultural heritage. She has authored/coauthored more than 70 research publications in these areas, including the monograph Moments and Moment Invariants in Pattern Recognition (Wiley, 2009). In 2003 Barbara Zitová received the Josef Hlavka Student Prize, the Otto Wichterle Premium of the Czech Academy of Sciences for young scientists in 2006, and in 2010 she was awarded by the SCOPUS 1000 Award for receiving more than 1000 citations of a single paper.

Preface xvii

Acknowledgements xxi

1 Motivation 1

1.1 Image analysis by computers 1

1.2 Humans, computers, and object recognition 4

1.3 Outline of the book 5

References 7

2 Introduction to Object Recognition 8

2.1 Feature space 8

2.1.1 Metric spaces and norms 9

2.1.2 Equivalence and partition 11

2.1.3 Invariants 12

2.1.4 Covariants 14

2.1.5 Invariant-less approaches 15

2.2 Categories of the invariants 15

2.2.1 Simple shape features 16

2.2.2 Complete visual features 18

2.2.3 Transformation coefficient features 20

2.2.4 Textural features 21

2.2.5 Wavelet-based features 23

2.2.6 Differential invariants 24

2.2.7 Point set invariants 25

2.2.8 Moment invariants 26

2.3 Classifiers 27

2.3.1 Nearest-neighbor classifiers 28

2.3.2 Support vector machines 31

2.3.3 Neural network classifiers 32

2.3.4 Bayesian classifier 34

2.3.5 Decision trees 35

2.3.6 Unsupervised classification 36

2.4 Performance of the classifiers 37

2.4.1 Measuring the classifier performance 37

2.4.2 Fusing classifiers 38

2.4.3 Reduction of the feature space dimensionality 38

2.5 Conclusion 40

References 41

3 2D Moment Invariants to Translation, Rotation, and Scaling 45

3.1 Introduction 45

3.1.1 Mathematical preliminaries 45

3.1.2 Moments 47

3.1.3 Geometric moments in 2D 48

3.1.4 Other moments 49

3.2 TRS invariants from geometric moments 50

3.2.1 Invariants to translation 50

3.2.2 Invariants to uniform scaling 51

3.2.3 Invariants to non-uniform scaling 52

3.2.4 Traditional invariants to rotation 54

3.3 Rotation invariants using circular moments 56

3.4 Rotation invariants from complex moments 57

3.4.1 Complex moments 57

3.4.2 Construction of rotation invariants 58

3.4.3 Construction of the basis 59

3.4.4 Basis of the invariants of the second and third orders 62

3.4.5 Relationship to the Hu invariants 63

3.5 Pseudoinvariants 67

3.6 Combined invariants to TRS and contrast stretching 68

3.7 Rotation invariants for recognition of symmetric objects 69

3.7.1 Logo recognition 75

3.7.2 Recognition of shapes with different fold numbers 75

3.7.3 Experiment with a baby toy 77

3.8 Rotation invariants via image normalization 81

3.9 Moment invariants of vector fields 86

3.10 Conclusion 92

References 92

4 3D Moment Invariants to Translation, Rotation, and Scaling 95

4.1 Introduction 95

4.2 Mathematical description of the 3D rotation 98

4.3 Translation and scaling invariance of 3D geometric moments 100

4.4 3D rotation invariants by means of tensors 101

4.4.1 Tensors 101

4.4.2 Rotation invariants 102

4.4.3 Graph representation of the invariants 103

4.4.4 The number of the independent invariants 104

4.4.5 Possible dependencies among the invariants 105

4.4.6 Automatic ge…