2D and 3D image analysis by moments /

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 o...

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Bibliographic Details
Main Authors:	Flusser, Jan (Author), Suk, Tomáš (Author), Zitová, Barbara (Author)
Format:	eBook
Language:	English
Published:	Chichester, West Sussex, United Kingdom : John Wiley & Sons, Ltd, 2017.
Subjects:	Invariants. Moment problems (Mathematics) Image analysis.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Cover
Title Page
Copyright
Dedication
Contents
Preface
Acknowledgements
Chapter 1 Motivation
1.1 Image analysis by computers
1.2 Humans, computers, and object recognition
1.3 Outline of the book
References
Chapter 2 Introduction to Object Recognition
2.1 Feature space
2.1.1 Metric spaces and norms
2.1.2 Equivalence and partition
2.1.3 Invariants
2.1.4 Covariants
2.1.5 Invariant-less approaches
2.2 Categories of the invariants
2.2.1 Simple shape features
2.2.2 Complete visual features
2.2.3 Transformation coefficient features
2.2.4 Textural features
2.2.5 Wavelet-based features
2.2.6 Differential invariants
2.2.7 Point set invariants
2.2.8 Moment invariants
2.3 Classifiers
2.3.1 Nearest-neighbor classifiers
2.3.2 Support vector machines
2.3.3 Neural network classifiers
2.3.4 Bayesian classifier
2.3.5 Decision trees
2.3.6 Unsupervised classification
2.4 Performance of the classifiers
2.4.1 Measuring the classifier performance
2.4.2 Fusing classifiers
2.4.3 Reduction of the feature space dimensionality
2.5 Conclusion
References
Chapter 3 2D Moment Invariants to Translation, Rotation, and Scaling
3.1 Introduction
3.1.1 Mathematical preliminaries
3.1.2 Moments
3.1.3 Geometric moments in 2D
3.1.4 Other moments
3.2 TRS invariants from geometric moments
3.2.1 Invariants to translation
3.2.2 Invariants to uniform scaling
3.2.3 Invariants to non-uniform scaling
3.2.4 Traditional invariants to rotation
3.3 Rotation invariants using circular moments
3.4 Rotation invariants from complex moments
3.4.1 Complex moments
3.4.2 Construction of rotation invariants
3.4.3 Construction of the basis
3.4.4 Basis of the invariants of the second and third orders
3.4.5 Relationship to the Hu invariants.
3.5 Pseudoinvariants
3.6 Combined invariants to TRS and contrast stretching
3.7 Rotation invariants for recognition of symmetric objects
3.7.1 Logo recognition
3.7.2 Recognition of shapes with different fold numbers
3.7.3 Experiment with a baby toy
3.8 Rotation invariants via image normalization
3.9 Moment invariants of vector fields
3.10 Conclusion
References
Chapter 4 3D Moment Invariants to Translation, Rotation, and Scaling
4.1 Introduction
4.2 Mathematical description of the 3D rotation
4.3 Translation and scaling invariance of 3D geometric moments
4.4 3D rotation invariants by means of tensors
4.4.1 Tensors
4.4.2 Rotation invariants
4.4.3 Graph representation of the invariants
4.4.4 The number of the independent invariants
4.4.5 Possible dependencies among the invariants
4.4.6 Automatic generation of the invariants by the tensor method
4.5 Rotation invariants from 3D complex moments
4.5.1 Translation and scaling invariance of 3D complex moments
4.5.2 Invariants to rotation by means of the group representation theory
4.5.3 Construction of the rotation invariants
4.5.4 Automated generation of the invariants
4.5.5 Elimination of the reducible invariants
4.5.6 The irreducible invariants
4.6 3D translation, rotation, and scale invariants via normalization
4.6.1 Rotation normalization by geometric moments
4.6.2 Rotation normalization by complex moments
4.7 Invariants of symmetric objects
4.7.1 Rotation and reflection symmetry in 3D
4.7.2 The influence of symmetry on 3D complex moments
4.7.3 Dependencies among the invariants due to symmetry
4.8 Invariants of 3D vector fields
4.9 Numerical experiments
4.9.1 Implementation details
4.9.2 Experiment with archeological findings
4.9.3 Recognition of generic classes.
4.9.4 Submarine recognition
robustness to noise test
4.9.5 Teddy bears
the experiment on real data
4.9.6 Artificial symmetric bodies
4.9.7 Symmetric objects from the Princeton Shape Benchmark
4.10 Conclusion
Appendix 4.A
Appendix 4.B
Appendix 4.C
References
Chapter 5 Affine Moment Invariants in 2D and 3D
5.1 Introduction
5.1.1 2D projective imaging of 3D world
5.1.2 Projective moment invariants
5.1.3 Affine transformation
5.1.4 2D Affine moment invariants-the history
5.2 AMIs derived from the Fundamental theorem
5.3 AMIs generated by graphs
5.3.1 The basic concept
5.3.2 Representing the AMIs by graphs
5.3.3 Automatic generation of the invariants by the graph method
5.3.4 Independence of the AMIs
5.3.5 The AMIs and tensors
5.4 AMIs via image normalization
5.4.1 Decomposition of the affine transformation
5.4.2 Relation between the normalized moments and the AMIs
5.4.3 Violation of stability
5.4.4 Affine invariants via half normalization
5.4.5 Affine invariants from complex moments
5.5 The method of the transvectants
5.6 Derivation of the AMIs from the Cayley-Aronhold equation
5.6.1 Manual solution
5.6.2 Automatic solution
5.7 Numerical experiments
5.7.1 Invariance and robustness of the AMIs
5.7.2 Digit recognition
5.7.3 Recognition of symmetric patterns
5.7.4 The children's mosaic
5.7.5 Scrabble tiles recognition
5.8 Affine invariants of color images
5.8.1 Recognition of color pictures
5.9 Affine invariants of 2D vector fields
5.10 3D affine moment invariants
5.10.1 The method of geometric primitives
5.10.2 Normalized moments in 3D
5.10.3 Cayley-Aronhold equation in 3D
5.11 Beyond invariants
5.11.1 Invariant distance measure between images
5.11.2 Moment matching.
5.11.3 Object recognition as a minimization problem
5.11.4 Numerical experiments
5.12 Conclusion
Appendix 5.A
Appendix 5.B
References
Chapter 6 Invariants to Image Blurring
6.1 Introduction
6.1.1 Image blurring-the sources and modeling
6.1.2 The need for blur invariants
6.1.3 State of the art of blur invariants
6.1.4 The chapter outline
6.2 An intuitive approach to blur invariants
6.3 Projection operators and blur invariants in Fourier domain
6.4 Blur invariants from image moments
6.5 Invariants to centrosymmetric blur
6.6 Invariants to circular blur
6.7 Invariants to N-FRS blur
6.8 Invariants to dihedral blur
6.9 Invariants to directional blur
6.10 Invariants to Gaussian blur
6.10.1 1D Gaussian blur invariants
6.10.2 Multidimensional Gaussian blur invariants
6.10.3 2D Gaussian blur invariants from complex moments
6.11 Invariants to other blurs
6.12 Combined invariants to blur and spatial transformations
6.12.1 Invariants to blur and rotation
6.12.2 Invariants to blur and affine transformation
6.13 Computational issues
6.14 Experiments with blur invariants
6.14.1 A simple test of blur invariance property
6.14.2 Template matching in satellite images
6.14.3 Template matching in outdoor images
6.14.4 Template matching in astronomical images
6.14.5 Face recognition on blurred and noisy photographs
6.14.6 Traffic sign recognition
6.15 Conclusion
Appendix 6.A
Appendix 6.B
Appendix 6.C
Appendix 6.D
Appendix 6.E
Appendix 6.F
Appendix 6.G
References
Chapter 7 2D and 3D Orthogonal Moments
7.1 Introduction
7.2 2D moments orthogonal on a square
7.2.1 Hypergeometric functions
7.2.2 Legendre moments
7.2.3 Chebyshev moments
7.2.4 Gaussian-Hermite moments
7.2.5 Other moments orthogonal on a square.
7.2.6 Orthogonal moments of a discrete variable
7.2.7 Rotation invariants from moments orthogonal on a square
7.3 2D moments orthogonal on a disk
7.3.1 Zernike and Pseudo-Zernike moments
7.3.2 Fourier-Mellin moments
7.3.3 Other moments orthogonal on a disk
7.4 Object recognition by Zernike moments
7.5 Image reconstruction from moments
7.5.1 Reconstruction by direct calculation
7.5.2 Reconstruction in the Fourier domain
7.5.3 Reconstruction from orthogonal moments
7.5.4 Reconstruction from noisy data
7.5.5 Numerical experiments with a reconstruction from OG moments
7.6 3D orthogonal moments
7.6.1 3D moments orthogonal on a cube
7.6.2 3D moments orthogonal on a sphere
7.6.3 3D moments orthogonal on a cylinder
7.6.4 Object recognition of 3D objects by orthogonal moments
7.6.5 Object reconstruction from 3D moments
7.7 Conclusion
References
Chapter 8 Algorithms for Moment Computation
8.1 Introduction
8.2 Digital image and its moments
8.2.1 Digital image
8.2.2 Discrete moments
8.3 Moments of binary images
8.3.1 Moments of a rectangle
8.3.2 Moments of a general-shaped binary object
8.4 Boundary-based methods for binary images
8.4.1 The methods based on Green's theorem
8.4.2 The methods based on boundary approximations
8.4.3 Boundary-based methods for 3D objects
8.5 Decomposition methods for binary images
8.5.1 The delta method
8.5.2 Quadtree decomposition
8.5.3 Morphological decomposition
8.5.4 Graph-based decomposition
8.5.5 Computing binary OG moments by means of decomposition methods
8.5.6 Experimental comparison of decomposition methods
8.5.7 3D decomposition methods
8.6 Geometric moments of graylevel images
8.6.1 Intensity slicing
8.6.2 Bit slicing
8.6.3 Approximation methods
8.7 Orthogonal moments of graylevel images.