Moments and Moment Invariants in Pattern Recognition

by Flusser, Jan; Zitova, Barbara; Suk, Tomas

• ISBN13: 9780470699874
• ISBN10: 0470699876
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-12-14
• Publisher: Wiley

Summary

Moments as projections of an image's intensity onto a proper polynomial basis can be applied to many different aspects of image processing. These include invariant pattern recognition, image normalization, image registration, focus/ defocus measurement, and watermarking. This book presents a survey of both recent and traditional image analysis and pattern recognition methods, based on image moments, and offers new concepts of invariants to linear filtering and implicit invariants. In addition to the theory, attention is paid to efficient algorithms for moment computation in a discrete domain, and to computational aspects of orthogonal moments. The authors also illustrate the theory through practical examples, demonstrating moment invariants in real applications across computer vision, remote sensing and medical imaging. Key features: Presents a systematic review of the basic definitions and properties of moments covering geometric moments and complex moments. Considers invariants to traditional transforms translation, rotation, scaling, and affine transform - from a new point of view, which offers new possibilities of designing optimal sets of invariants. Reviews and extends a recent field of invariants with respect to convolution/blurring. Introduces implicit moment invariants as a tool for recognizing elastically deformed objects. Compares various classes of orthogonal moments (Legendre, Zernike, Fourier-Mellin, Chebyshev, among others) and demonstrates their application to image reconstruction from moments. Offers comprehensive advice on the construction of various invariants illustrated with practical examples. Includes an accompanying website providing efficient numerical algorithms for moment computation and for constructing invariants of various kinds, with about 250 slides suitable for a graduate university course.Moments and Moment Invariants in Pattern Recognition is ideal for researchers and engineers involved in pattern recognition in medical imaging, remote sensing, robotics and computer vision. Post graduate students in image processing and pattern recognition will also find the book of interest.

Author Biography

Jan Flusser is a full professor of Computer Science at the Czech Technical University and the Charles University, Prague.

Table of Contents

Authors' biographies	p. xi
Preface	p. xiii
Acknowledgments	p. xv
Introduction to moments	p. 1
Motivation	p. 1
What are invariants?	p. 3
Categories of invariant	p. 4
What are moments?	p. 6
Geometric and complex moments	p. 6
Orthogonal moments	p. 7
Outline of the book	p. 8
References	p. 9
Moment invariants to translation, rotation and scaling	p. 13
Introduction	p. 13
Invariants to translation	p. 13
Invariants to uniform scaling	p. 14
Traditional invariants to rotation	p. 15
Rotation invariants from complex moments	p. 17
Construction of rotation invariants	p. 17
Construction of the basis	p. 19
Basis of invariants of the second and third orders	p. 22
Relationship to the Hu invariants	p. 22
Pseudoinvariants	p. 26
Combined invariants to TRS and contrast changes	p. 27
Rotation invariants for recognition of symmetric objects	p. 29
Logo recognition	p. 32
Recognition of simple shapes	p. 33
Experiment with a baby toy	p. 34
Rotation invariants via image normalization	p. 38
Invariants to nonuniform scaling	p. 42
TRS invariants in 3D	p. 43
Conclusion	p. 45
References	p. 45
Affine moment invariants	p. 49
Introduction	p. 49
Projective imaging of a 3D world	p. 49
Projective moment invariants	p. 50
Affine transformation	p. 52
AMJs	p. 53
AMIs derived from the Fundamental theorem	p. 54
AMIs generated by graphs	p. 55
The basic concept	p. 55
Representing the invariants by graphs	p. 57
Independence of the AMIs	p. 58
The AMIs and tensors	p. 64
Robustness of the AMIs	p. 66
AMIs via image normalization	p. 67
Decomposition of the affine transform	p. 70
Violation of stability	p. 74
Relation between the normalized moments and the AMIs	p. 74
Affine invariants via half normalization	p. 76
Affine invariants from complex moments	p. 76
Derivation of the AMIs from the Cayley-Aronhold equation	p. 79
Manual solution	p. 79
Automatic solution	p. 81
Numerical experiments	p. 84
Digit recognition	p. 84
Recognition of symmetric patterns	p. 87
The children's mosaic	p. 87
Affine invariants of color images	p. 92
Generalization to three dimensions	p. 95
Method of geometric primitives	p. 96
Normalized moments in 3D	p. 98
Half normalization in 3D	p. 102
Direct solution of the Cayley-Aronhold equation	p. 104
Conclusion	p. 104
Appendix	p. 105
References	p. 109
Implicit invariants to elastic transformations	p. 113
Introduction	p. 113
General moments under a polynomial transform	p. 116
Explicit and implicit invariants	p. 117
Implicit invariants as a minimization task	p. 119
Numerical experiments	p. 120
Invariance and robustness test	p. 121
ALOI classification experiment	p. 122
Character recognition on a bottle	p. 122
Conclusion	p. 125
References	p. 126
Invariants to convolution	p. 129
Introduction	p. 129
Blur invariants for centrosymmetric PSFs	p. 133
Template matching experiment	p. 138
Invariants to linear motion blur	p. 139
Extension to n dimensions	p. 143
Possible applications and limitations	p. 144
Blur invariants for W-fold symmetric PSFs	p. 145
Blur invariants for circularly symmetric PSFs	p. 146
Blur invariants for Gaussian PSFs	p. 147
Combined invariants	p. 148
Combined invariants to convolution and rotation	p. 149
Combined invariants to convolution and affine transform	p. 150
Conclusion	p. 151
Appendix	p. 151
References	p. 162
Orthogonal moments	p. 165
Introduction	p. 165
Moments orthogonal on a rectangle	p. 166
Hypergeometric functions	p. 167
Legendre moments	p. 168
Chebyshev moments	p. 171
Other moments orthogonal on a rectangle	p. 173
OG moments of a discrete variable	p. 178
Moments orthogonal on a disk	p. 186
Zernike and Pseudo-Zernike moments	p. 186
Orthogonal Fourier-Mellin moments	p. 192
Other moments orthogonal on a disk	p. 194
Object recognition by ZMs	p. 196
Image reconstruction from moments	p. 197
Reconstruction by the direct calculation	p. 199
Reconstruction in the Fourier domain	p. 200
Reconstruction from OG moments	p. 201
Reconstruction from noisy data	p. 204
Numerical experiments with image reconstruction from OG moments	p. 204
Three-dimensional OG moments	p. 206
Conclusion	p. 209
References	p. 209
Algorithms for moment computation	p. 213
Introduction	p. 213
Moments in a discrete domain	p. 213
Geometric moments of binary images	p. 215
Decomposition methods for binary images	p. 216
Boundary-based methods for binary images	p. 219
Other methods for binary images	p. 221
Geometric moments of graylevel images	p. 222
Intensity slicing	p. 222
Approximation methods	p. 223
Efficient methods for calculating OG moments	p. 225
Methods using recurrent relations	p. 225
Decomposition methods	p. 228
Boundary-based methods	p. 230
Generalization to n dimensions	p. 230
Conclusion	p. 231
References	p. 232
Applications	p. 235
Introduction	p. 235
Object representation and recognition	p. 235
Image registration	p. 240
Registration of satellite images	p. 241
Image registration for image fusion	p. 246
Robot navigation	p. 250
Indoor robot navigation based on circular landmarks	p. 251
Recognition of landmarks using fish-eye lens camera	p. 253
Image retrieval	p. 257
Watermarking	p. 259
Watermarking based on the geometric moments	p. 260
Medical imaging	p. 263
Landmark recognition in the scoliosis study	p. 264
Forensic applications	p. 267
Detection of near-duplicated image regions	p. 267
Miscellaneous applications	p. 271
Noise-resistant optical flow estimation	p. 272
Focus measure	p. 272
Edge detection	p. 275
Gas-liquid flow categorization	p. 276
3D objects visualization	p. 276
Conclusion	p. 276
References	p. 277
Conclusion	p. 289
Index	p. 291
Table of Contents provided by Ingram. All Rights Reserved.