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(s): Jan Flusser, Barbara Zitova, Tomas Suk
Publisher: Wiley
Year: 2009
Language: English
Pages: 314
Contents......Page 9
Authors’ biographies......Page 13
Preface......Page 15
Acknowledgments......Page 17
1.1 Motivation......Page 19
1.2 What are invariants?......Page 21
1.2.1 Categories of invariant......Page 22
1.3.1 Geometric and complex moments......Page 24
1.3.2 Orthogonal moments......Page 25
1.4 Outline of the book......Page 26
References......Page 27
2.1.1 Invariants to translation......Page 31
2.1.2 Invariants to uniform scaling......Page 32
2.1.3 Traditional invariants to rotation......Page 33
2.2.1 Construction of rotation invariants......Page 35
2.2.2 Construction of the basis......Page 37
2.2.4 Relationship to the Hu invariants......Page 40
2.3 Pseudoinvariants......Page 44
2.4 Combined invariants to TRS and contrast changes......Page 45
2.5 Rotation invariants for recognition of symmetric objects......Page 47
2.5.1 Logo recognition......Page 50
2.5.2 Recognition of simple shapes......Page 51
2.5.3 Experiment with a baby toy......Page 52
2.6 Rotation invariants via image normalization......Page 56
2.7 Invariants to nonuniform scaling......Page 60
2.8 TRS invariants in 3D......Page 61
References......Page 63
3.1.1 Projective imaging of a 3D world......Page 67
3.1.2 Projective moment invariants......Page 68
3.1.3 Affine transformation......Page 70
3.1.4 AMIs......Page 71
3.2 AMIs derived from the Fundamental theorem......Page 72
3.3.1 The basic concept......Page 73
3.3.2 Representing the invariants by graphs......Page 75
3.3.3 Independence of the AMIs......Page 76
3.3.4 The AMIs and tensors......Page 82
3.3.5 Robustness of the AMIs......Page 84
3.4 AMIs via image normalization......Page 85
3.4.1 Decomposition of the affine transform......Page 88
3.4.3 Relation between the normalized moments and the AMIs......Page 92
3.4.5 Affine invariants from complex moments......Page 94
3.5.1 Manual solution......Page 97
3.5.2 Automatic solution......Page 99
3.6.1 Digit recognition......Page 102
3.6.3 The children’s mosaic......Page 105
3.7 Affine invariants of color images......Page 110
3.8 Generalization to three dimensions......Page 113
3.8.1 Method of geometric primitives......Page 114
3.8.2 Normalized moments in 3D......Page 116
3.8.3 Half normalization in 3D......Page 120
3.9 Conclusion......Page 122
Appendix......Page 123
References......Page 127
4.1 Introduction......Page 131
4.2 General moments under a polynomial transform......Page 134
4.3 Explicit and implicit invariants......Page 135
4.4 Implicit invariants as a minimization task......Page 137
4.5 Numerical experiments......Page 138
4.5.1 Invariance and robustness test......Page 139
4.5.3 Character recognition on a bottle......Page 140
4.6 Conclusion......Page 143
References......Page 144
5.1 Introduction......Page 147
5.2 Blur invariants for centrosymmetric PSFs......Page 151
5.2.1 Template matching experiment......Page 156
5.2.2 Invariants to linear motion blur......Page 157
5.2.3 Extension to n dimensions......Page 161
5.2.4 Possible applications and limitations......Page 162
5.3 Blur invariants for N-fold symmetric PSFs......Page 163
5.3.1 Blur invariants for circularly symmetric PSFs......Page 164
5.3.2 Blur invariants for Gaussian PSFs......Page 165
5.4 Combined invariants......Page 166
5.4.1 Combined invariants to convolution and roation......Page 167
5.4.2 Combined invariants to convolution and affine transform......Page 168
Appendix......Page 169
References......Page 180
6.1 Introduction......Page 183
6.2 Moments orthogonal on a rectangle......Page 184
6.2.1 Hypergeometric functions......Page 185
6.2.2 Legendre moments......Page 186
6.2.3 Chebyshev moments......Page 189
6.2.4 Other moments orthogonal on a rectangle......Page 191
6.2.5 OG moments of a discrete variable......Page 196
6.3.1 Zernike and Pseudo-Zernike moments......Page 204
6.3.2 Orthogonal Fourier–Mellin moments......Page 210
6.3.3 Other moments orthogonal on a disk......Page 212
6.4 Object recognition by ZMs......Page 214
6.5 Image reconstruction from moments......Page 215
6.5.1 Reconstruction by the direct calculation......Page 217
6.5.2 Reconstruction in the Fourier domain......Page 218
6.5.3 Reconstruction from OG moments......Page 219
6.5.5 Numerical experiments with image reconstruction from OG moments......Page 222
6.6 Three-dimensional OG moments......Page 224
References......Page 227
7.2 Moments in a discrete domain......Page 231
7.3 Geometric moments of binary images......Page 233
7.3.1 Decomposition methods for binary images......Page 234
7.3.2 Boundary-based methods for binary images......Page 237
7.3.3 Other methods for binary images......Page 239
7.4.1 Intensity slicing......Page 240
7.4.2 Approximation methods......Page 241
7.5.1 Methods using recurrent relations......Page 243
7.5.2 Decomposition methods......Page 246
7.6 Generalization to n dimensions......Page 248
7.7 Conclusion......Page 249
References......Page 250
8.2 Object representation and recognition......Page 253
8.3 Image registration......Page 258
8.3.1 Registration of satellite images......Page 259
8.3.2 Image registration for image fusion......Page 264
8.4 Robot navigation......Page 268
8.4.1 Indoor robot navigation based on circular landmarks......Page 269
8.4.2 Recognition of landmarks using fish-eye lens camera......Page 271
8.5 Image retrieval......Page 275
8.6 Watermarking......Page 277
8.6.1 Watermarking based on the geometric moments......Page 278
8.7 Medical imaging......Page 281
8.7.1 Landmark recognition in the scoliosis study......Page 282
8.8.1 Detection of near-duplicated image regions......Page 285
8.9 Miscellaneous applications......Page 289
8.9.2 Focus measure......Page 290
8.9.3 Edge detection......Page 293
8.10 Conclusion......Page 294
References......Page 295
9 Conclusion......Page 307
Index......Page 309
