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E-raamat: 2D and 3D Image Analysis by Moments

(Inst of Information Theory & Automation), (Inst of Information Theory & Automation), (Inst of Information Theory & Automation)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 15-Nov-2016
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119039365
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2D and 3D Image Analysis by MomentsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 15-Nov-2016
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119039365
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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.

Preface xvii
Acknowledgements xxi
1 Motivation 1(7)
1.1 Image analysis by computers
1(3)
1.2 Humans, computers, and object recognition
4(1)
1.3 Outline of the book
5(2)
References
7(1)
2 Introduction to Object Recognition 8(37)
2.1 Feature space
8(7)
2.1.1 Metric spaces and norms
9(2)
2.1.2 Equivalence and partition
11(1)
2.1.3 Invariants
12(2)
2.1.4 Covariants
14(1)
2.1.5 Invariant-less approaches
15(1)
2.2 Categories of the invariants
15(12)
2.2.1 Simple shape features
16(2)
2.2.2 Complete visual features
18(2)
2.2.3 Transformation coefficient features
20(1)
2.2.4 Textural features
21(2)
2.2.5 Wavelet-based features
23(1)
2.2.6 Differential invariants
24(1)
2.2.7 Point set invariants
25(1)
2.2.8 Moment invariants
26(1)
2.3 Classifiers
27(10)
2.3.1 Nearest-neighbor classifiers
28(3)
2.3.2 Support vector machines
31(1)
2.3.3 Neural network classifiers
32(2)
2.3.4 Bayesian classifier
34(1)
2.3.5 Decision trees
35(1)
2.3.6 Unsupervised classification
36(1)
2.4 Performance of the classifiers
37(3)
2.4.1 Measuring the classifier performance
37(1)
2.4.2 Fusing classifiers
38(1)
2.4.3 Reduction of the feature space dimensionality
38(2)
2.5 Conclusion
40(1)
References
41(4)
3 2D Moment Invariants to Translation, Rotation, and Scaling 45(50)
3.1 Introduction
45(5)
3.1.1 Mathematical preliminaries
45(2)
3.1.2 Moments
47(1)
3.1.3 Geometric moments in 2D
48(1)
3.1.4 Other moments
49(1)
3.2 TRS invariants from geometric moments
50(6)
3.2.1 Invariants to translation
50(1)
3.2.2 Invariants to uniform scaling
51(1)
3.2.3 Invariants to non-uniform scaling
52(2)
3.2.4 Traditional invariants to rotation
54(2)
3.3 Rotation invariants using circular moments
56(1)
3.4 Rotation invariants from complex moments
57(10)
3.4.1 Complex moments
57(1)
3.4.2 Construction of rotation invariants
58(1)
3.4.3 Construction of the basis
59(3)
3.4.4 Basis of the invariants of the second and third orders
62(1)
3.4.5 Relationship to the Hu invariants
63(4)
3.5 Pseudoinvariants
67(1)
3.6 Combined invariants to TRS and contrast stretching
68(1)
3.7 Rotation invariants for recognition of symmetric objects
69(12)
3.7.1 Logo recognition
75(1)
3.7.2 Recognition of shapes with different fold numbers
75(2)
3.7.3 Experiment with a baby toy
77(4)
3.8 Rotation invariants via image normalization
81(5)
3.9 Moment invariants of vector fields
86(6)
3.10 Conclusion
92(1)
References
92(3)
4 3D Moment Invariants to Translation, Rotation, and Scaling 95(68)
4.1 Introduction
95(3)
4.2 Mathematical description of the 3D rotation
98(2)
4.3 Translation and scaling invariance of 3D geometric moments
100(1)
4.4 3D rotation invariants by means of tensors
101(7)
4.4.1 Tensors
101(1)
4.4.2 Rotation invariants
102(1)
4.4.3 Graph representation of the invariants
103(1)
4.4.4 The number of the independent invariants
104(1)
4.4.5 Possible dependencies among the invariants
105(1)
4.4.6 Automatic generation of the invariants by the tensor method
106(2)
4.5 Rotation invariants from 3D complex moments
108(11)
4.5.1 Translation and scaling invariance of 3D complex moments
112(1)
4.5.2 Invariants to rotation by means of the group representation theory
112(3)
4.5.3 Construction of the rotation invariants
115(2)
4.5.4 Automated generation of the invariants
117(1)
4.5.5 Elimination of the reducible invariants
118(1)
4.5.6 The irreducible invariants
118(1)
4.6 3D translation, rotation, and scale invariants via normalization
119(5)
4.6.1 Rotation normalization by geometric moments
120(3)
4.6.2 Rotation normalization by complex moments
123(1)
4.7 Invariants of symmetric objects
124(7)
4.7.1 Rotation and reflection symmetry in 3D
124(4)
4.7.2 The influence of symmetry on 3D complex moments
128(2)
4.7.3 Dependencies among the invariants due to symmetry
130(1)
4.8 Invariants of 3D vector fields
131(1)
4.9 Numerical experiments
131(16)
4.9.1 Implementation details
131(2)
4.9.2 Experiment with archeological findings
133(2)
4.9.3 Recognition of generic classes
135(2)
4.9.4 Submarine recognition-robustness to noise test
137(4)
4.9.5 Teddy bears-the experiment on real data
141(1)
4.9.6 Artificial symmetric bodies
142(1)
4.9.7 Symmetric objects from the Princeton Shape Benchmark
143(4)
4.10 Conclusion
147(1)
Appendix 4.A
148(8)
Appendix 4.B
156(2)
Appendix 4.C
158(2)
References
160(3)
5 Affine Moment Invariants in 2D and 3D 163(74)
5.1 Introduction
163(7)
5.1.1 2D projective imaging of 3D world
164(1)
5.1.2 Projective moment invariants
165(2)
5.1.3 Affine transformation
167(1)
5.1.4 2D Affine moment invariants-the history
168(2)
5.2 AMIs derived from the Fundamental theorem
170(1)
5.3 AMIs generated by graphs
171(10)
5.3.1 The basic concept
172(1)
5.3.2 Representing the AMIs by graphs
173(1)
5.3.3 Automatic generation of the invariants by the graph method
173(1)
5.3.4 Independence of the AMIs
174(6)
5.3.5 The AMIs and tensors
180(1)
5.4 AMIs via image normalization
181(9)
5.4.1 Decomposition of the affine transformation
182(3)
5.4.2 Relation between the normalized moments and the AMIs
185(1)
5.4.3 Violation of stability
186(1)
5.4.4 Affine invariants via half normalization
187(1)
5.4.5 Affine invariants from complex moments
187(3)
5.5 The method of the transvectants
190(5)
5.6 Derivation of the AMIs from the Cayley-Aronhold equation
195(6)
5.6.1 Manual solution
195(3)
5.6.2 Automatic solution
198(3)
5.7 Numerical experiments
201(13)
5.7.1 Invariance and robustness of the AMIs
201(1)
5.7.2 Digit recognition
201(3)
5.7.3 Recognition of symmetric patterns
204(4)
5.7.4 The children's mosaic
208(2)
5.7.5 Scrabble tiles recognition
210(4)
5.8 Affine invariants of color images
214(4)
5.8.1 Recognition of color pictures
217(1)
5.9 Affine invariants of 2D vector fields
218(3)
5.10 3D affine moment invariants
221(4)
5.10.1 The method of geometric primitives
222(2)
5.10.2 Normalized moments in 3D
224(1)
5.10.3 Cayley-Aronhold equation in 3D
225(1)
5.11 Beyond invariants
225(6)
5.11.1 Invariant distance measure between images
225(2)
5.11.2 Moment matching
227(2)
5.11.3 Object recognition as a minimization problem
229(1)
5.11.4 Numerical experiments
229(2)
5.12 Conclusion
231(1)
Appendix 5.A
232(1)
Appendix 5.B
233(1)
References
234(3)
6 Invariants to Image Blurring 237(83)
6.1 Introduction
237(10)
6.1.1 Image blurring-the sources and modeling
237(2)
6.1.2 The need for blur invariants
239(1)
6.1.3 State of the art of blur invariants
239(7)
6.1.4 The chapter outline
246(1)
6.2 An intuitive approach to blur invariants
247(2)
6.3 Projection operators and blur invariants in Fourier domain
249(3)
6.4 Blur invariants from image moments
252(2)
6.5 Invariants to centrosymmetric blur
254(2)
6.6 Invariants to circular blur
256(3)
6.7 Invariants to N-FRS blur
259(6)
6.8 Invariants to dihedral blur
265(4)
6.9 Invariants to directional blur
269(3)
6.10 Invariants to Gaussian blur
272(8)
6.10.1 1D Gaussian blur invariants
274(4)
6.10.2 Multidimensional Gaussian blur invariants
278(1)
6.10.3 2D Gaussian blur invariants from complex moments
279(1)
6.11 Invariants to other blurs
280(2)
6.12 Combined invariants to blur and spatial transformations
282(2)
6.12.1 Invariants to blur and rotation
282(1)
6.12.2 Invariants to blur and affine transformation
283(1)
6.13 Computational issues
284(1)
6.14 Experiments with blur invariants
285(17)
6.14.1 A simple test of blur invariance property
285(1)
6.14.2 Template matching in satellite images
286(5)
6.14.3 Template matching in outdoor images
291(1)
6.14.4 Template matching in astronomical images
291(1)
6.14.5 Face recognition on blurred and noisy photographs
292(2)
6.14.6 Traffic sign recognition
294(8)
6.15 Conclusion
302(1)
Appendix 6.A
303(1)
Appendix 6.B
304(2)
Appendix 6.C
306(2)
Appendix 6.D
308(2)
Appendix 6.E
310(1)
Appendix 6.F
310(1)
Appendix 6.G
311(4)
References
315(5)
7 2D and 3D Orthogonal Moments 320(78)
7.1 Introduction
320(2)
7.2 2D moments orthogonal on a square
322(29)
7.2.1 Hypergeometric functions
323(1)
7.2.2 Legendre moments
324(3)
7.2.3 Chebyshev moments
327(4)
7.2.4 Gaussian-Hermite moments
331(3)
7.2.5 Other moments orthogonal on a square
334(4)
7.2.6 Orthogonal moments of a discrete variable
338(10)
7.2.7 Rotation invariants from moments orthogonal on a square
348(3)
7.3 2D moments orthogonal on a disk
351(12)
7.3.1 Zernike and Pseudo-Zernike moments
352(6)
7.3.2 Fourier-Mellin moments
358(3)
7.3.3 Other moments orthogonal on a disk
361(2)
7.4 Object recognition by Zernike moments
363(2)
7.5 Image reconstruction from moments
365(12)
7.5.1 Reconstruction by direct calculation
367(2)
7.5.2 Reconstruction in the Fourier domain
369(1)
7.5.3 Reconstruction from orthogonal moments
370(3)
7.5.4 Reconstruction from noisy data
373(1)
7.5.5 Numerical experiments with a reconstruction from OG moments
373(4)
7.6 3D orthogonal moments
377(12)
7.6.1 3D moments orthogonal on a cube
380(1)
7.6.2 3D moments orthogonal on a sphere
381(2)
7.6.3 3D moments orthogonal on a cylinder
383(1)
7.6.4 Object recognition of 3D objects by orthogonal moments
383(4)
7.6.5 Object reconstruction from 3D moments
387(2)
7.7 Conclusion
389(1)
References
389(9)
8 Algorithms for Moment Computation 398(50)
8.1 Introduction
398(1)
8.2 Digital image and its moments
399(3)
8.2.1 Digital image
399(1)
8.2.2 Discrete moments
400(2)
8.3 Moments of binary images
402(2)
8.3.1 Moments of a rectangle
402(1)
8.3.2 Moments of a general-shaped binary object
403(1)
8.4 Boundary-based methods for binary images
404(6)
8.4.1 The methods based on Green's theorem
404(2)
8.4.2 The methods based on boundary approximations
406(1)
8.4.3 Boundary-based methods for 3D objects
407(3)
8.5 Decomposition methods for binary images
410(18)
8.5.1 The "delta" method
412(1)
8.5.2 Quadtree decomposition
413(2)
8.5.3 Morphological decomposition
415(1)
8.5.4 Graph-based decomposition
416(4)
8.5.5 Computing binary OG moments by means of decomposition methods
420(2)
8.5.6 Experimental comparison of decomposition methods
422(1)
8.5.7 3D decomposition methods
423(5)
8.6 Geometric moments of graylevel images
428(7)
8.6.1 Intensity slicing
429(1)
8.6.2 Bit slicing
430(3)
8.6.3 Approximation methods
433(2)
8.7 Orthogonal moments of graylevel images
435(5)
8.7.1 Recurrent relations for moments orthogonal on a square
435(1)
8.7.2 Recurrent relations for moments orthogonal on a disk
436(2)
8.7.3 Other methods
438(2)
8.8 Conclusion
440(1)
Appendix 8.A
441(2)
References
443(5)
9 Applications 448(70)
9.1 Introduction
448(1)
9.2 Image understanding
448(11)
9.2.1 Recognition of animals
449(1)
9.2.2 Face and other human parts recognition
450(3)
9.2.3 Character and logo recognition
453(1)
9.2.4 Recognition of vegetation and of microscopic natural structures
454(1)
9.2.5 Traffic-related recognition
455(1)
9.2.6 Industrial recognition
456(1)
9.2.7 Miscellaneous applications
457(2)
9.3 Image registration
459(11)
9.3.1 Landmark-based registration
460(7)
9.3.2 Landmark-free registration methods
467(3)
9.4 Robot and autonomous vehicle navigation and visual servoing
470(4)
9.5 Focus and image quality measure
474(2)
9.6 Image retrieval
476(5)
9.7 Watermarking
481(5)
9.8 Medical imaging
486(3)
9.9 Forensic applications
489(7)
9.10 Miscellaneous applications
496(5)
9.10.1 Noise resistant optical flow estimation
496(1)
9.10.2 Edge detection
497(1)
9.10.3 Description of solar flares
498(1)
9.10.4 Gas-liquid flow categorization
499(1)
9.10.5 3D object visualization
500(1)
9.10.6 Object tracking
500(1)
9.11 Conclusion
501(1)
References
501(17)
10 Conclusion 518(3)
10.1 Summary of the book
518(1)
10.2 Pros and cons of moment invariants
519(1)
10.3 Outlook to the future
520(1)
Index 521
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).

Tomá 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.
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