2D and 3D Image Analysis by Moments. (2016)

• Record Type: Book
• Further Information: Note: Jan Flusser, Tomas Suk, Barbara Zitova.
• Authors: Flusser, Jan; Suk, Tomáš; Zitová, Barbara
• Contents: 1 motivation 7 1.1 Image analysis by computers 7 1.2 Humans, computers, and object recognition 10 1.3 Outline of the book 11 References 13 2 Introduction to Object Recognition 17 2.1 Feature space 17 2.1.1 Metric spaces and norms 18 2.1.2 Equivalence and partition 20 2.1.3 Invariants 22 2.1.4 Covariants 24 2.1.5 Invariant-less approaches 24 2.2 Categories of the invariants 24 2.2.1 Simple shape features 25 2.2.2 Complete visual features 27 2.2.3 Transformation coefficient features 32 2.2.4 Textural features 32 2.2.5 Wavelet-based features 34 2.2.6 Differential invariants 35 2.2.7 Point set invariants 37 2.2.8 Moment invariants 37 2.3 Classifiers 38 2.3.1 Nearest-neighbor classifiers 40 2.3.2 Support vector machines 43 2.3.3 Neural network classifiers 44 2.3.4 Bayesian classifier 46 2.3.5 Decision trees 47 2.3.6 Unsupervised classification 48 2.4 Performance of the classifiers 49 2.4.1 Measuring the classifier performance 49 2.4.2 Fusing classifiers 50 2.4.3 Reduction of the feature space dimensionality 50 2.5 Conclusion 53 References 53 3 2D Moment Invariants to Translation, Rotation, and Scaling 63 3.1 Introduction 63 3.1.1 Mathematical preliminaries 63 3.1.2 Moments 65 3.1.3 Geometric moments in 2D 66 3.1.4 Other moments 67 3.2 TRS invariants from geometric moments 68 3.2.1 Invariants to translation 68 3.2.2 Invariants to uniform scaling 69 3.2.3 Invariants to non-uniform scaling 70 3.2.4 Traditional invariants to rotation 72 3.3 Rotation invariants using circular moments 74 3.4 Rotation invariants from complex moments 75 3.4.1 Complex moments 75 3.4.2 Construction of rotation invariants 76 3.4.3 Construction of the basis 77 3.4.4 Basis of the invariants of the 2nd and 3rd orders 80 3.4.5 Relationship to the Hu invariants 82 3.5 Pseudoinvariants 84 3.6 Combined invariants to TRS and contrast 85 3.7 Rotation invariants of symmetric objects 87 3.7.1 Logo recognition 93 3.7.2 Recognition of shapes with different fold numbers 95 3.7.3 Experiment with a baby toy 100 3.8 Rotation invariants via image normalization 101 3.9 Moment invariants of vector fields 106 3.10 Conclusion 113 References 113 4 3D Moment Invariants to Translation, Rotation, and Scaling 119 4.1 Introduction 119 4.2 Mathematical description of the 3D rotation 122 4.3 Translation and scaling invariance of 3D moments 124 4.4 3D rotation invariants by means of tensors 125 4.4.1 Tensors 125 4.4.2 Rotation invariants 126 4.4.3 Graph representation of the invariants 127 4.4.4 The number of the independent invariants 128 4.4.5 Possible dependencies among the invariants 129 4.4.6 Automatic generation of the invariants by the tensor method 130 4.5 Rotation invariants from 3D complex moments 132 4.5.1 Translation and scaling invariance of 3D complex moments 136 4.5.2 Invariants to rotation by means of the group representation theory137 4.5.3 Construction of the rotation invariants 140 4.5.4 Automated generation of the invariants 141 4.5.5 Elimination of the reducible invariants 142 4.5.6 The irreducible invariants 143 4.6 3D translation, rotation, and scale invariants via normalization 144 4.6.1 Rotation normalization by geometric moments 144 4.6.2 Rotation normalization by complex moments 147 4.7 Invariants of symmetric objects 148 4.7.1 Rotation and reflection symmetry in 3D 149 4.7.2 The influence of symmetry on 3D complex moments 154 4.7.3 Dependencies among the invariants due to the symmetry 155 4.8 Invariants of 3D vector fields 156 4.9 Numerical Experiments 157 4.9.1 Implementation details 157 4.9.2 Experiment with archeological findings 158 4.9.3 Recognition of generic classes 161 4.9.4 Submarine recognition – robustness to noise test 163 4.9.5 Teddy bears – the experiment on real data 167 4.9.6 Artificial symmetric bodies 168 4.9.7 Symmetric objects from the Princeton Shape Benchmark 172 4.10 Conclusion 174 Appendix 175 References 186 5 Affine Moment Invariants in 2D and 3D 191 5.1 Introduction 191 5.1.1 2D projective imaging of 3D world 192 5.1.2 Projective moment invariants 192 5.1.3 Affine transformation 195 5.1.4 2D Affine moment invariants – the history 196 5.2 AMIs derived from the Fundamental theorem 198 5.3 AMIs generated by graphs 199 5.3.1 The basic concept 199 5.3.2 Representing the AMIs by graphs 201 5.3.3 Automatic generation of the invariants by the graph method 201 5.3.4 Independence of the AMI’s 202 5.3.5 The AMIs and tensors 208 5.4 AMIs via image normalization 208 5.4.1 Decomposition of the affine transformation 210 5.4.2 Relation between the normalized moments and the AMIs 213 5.4.3 Violation of stability 213 5.4.4 Affine invariants via half normalization 214 5.4.5 Affine invariants from complex moments 214 5.5 The method of the transvectants 217 5.6 Derivation of the AMIs from the Cayley-Aronhold equation 222 5.6.1 Manual solution 222 5.6.2 Automatic solution 224 5.7 Numerical experiments 227 5.7.1 Invariance and robustness of the AMIs 227 5.7.2 Digit recognition 228 5.7.3 Recognition of symmetric patterns 229 5.7.4 The children’s mosaic 230 5.7.5 Scrabble tiles recognition 244 5.8 Affine invariants of color images 247 5.8.1 Recognition of color pictures 249 5.9 Affine invariants of 2D vector fields 253 5.10 3D affine moment invariants 255 5.10.1 The method of geometric primitives 255 5.10.2 Normalized moments in 3D 257 5.10.3 Cayley-Aronhold equation in 3D 258 5.11 Beyond invariants 258 5.11.1 Invariant distance measure between images 258 5.11.2 Moment matching 260 5.11.3 Object recognition as a minimization problem 262 5.11.4 Numerical experiments 263 5.12 Conclusion 264 Appendix 265 References 267 6 Invariants to Image Blurring 273 6.1 Introduction 273 6.1.1 Image blurring – the sources and modeling 273 6.1.2 The need for blur invariants 274 6.1.3 State of the art of blur invariants 276 6.1.4 The Chapter outline 283 6.2 An intuitive approach to blur invariants 283 6.3 Projection operators in Fourier domain 286 6.4 Blur invariants from image moments 289 6.5 Invariants to centrosymmetric blur 291 6.6 Invariants to circular blur 292 6.7 Invariants to N-FRS blur 294 6.8 Invariants to dihedral blur 304 6.9 Invariants to directional blur 309 6.10 Invariants to Gaussian blur 313 6.10.1 1D Gaussian blur invariants 315 6.10.2 Multidimensional Gaussian blur invariants 318 6.10.3 2D Gaussian blur invariants from complex moments 320 6.11 Invariants to other blurs 321 6.12 Combined invariants to blur and spatial tr 322 6.12.1 Invariants to blur and rotation 323 6.12.2 Invariants to convolution and affine transform 324 6.13 Computational issues 325 6.14 Experiments with blur invariants 326 6.14.1 A simple test of blur invariance property 326 6.14.2 Template matching in satelli
• Edition: 1st
• Publisher Details: Wiley
• Publication Date: 2016
• Extent: 1 online resource (560 pages)
• Languages: English
• ISBNs: 9781119039365
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.