Handbook of Computer Vision and Applications, V3

Introduction......Page 26
Signal processing for computer vision......Page 27
Pattern recognition for computer vision......Page 28
Computational complexity and fast algorithms......Page 29
Performance evaluation of algorithms......Page 30
References......Page 31
Signal Representation......Page 32
Continuous and Digital Signals......Page 34
Types of signals......Page 35
Unified description......Page 36
Multichannel signals......Page 37
Regular two-dimensional lattices......Page 38
Regular higher-dimensional lattices......Page 41
Metric in digital images......Page 42
Neighborhood relations......Page 44
Errors in object position and geometry......Page 45
Relation between continuous and discrete signals......Page 48
Image formation......Page 49
Sampling theorem......Page 50
Reconstruction from samples......Page 53
Equidistant quantization......Page 55
Unsigned or signed representation......Page 56
Nonequidistant quantization......Page 57
References......Page 59
Introduction......Page 60
Significance of the Fourier transform (FT)......Page 62
Dynamical range and resolution of the FT......Page 63
One-dimensional FT......Page 66
Basic properties......Page 68
Important transform pairs......Page 74
The discrete Fourier transform (DFT)......Page 75
One-dimensional DFT......Page 76
Multidimensional DFT......Page 78
Basic properties......Page 79
One-dimensional FFT algorithms......Page 82
Multidimensional FFT algorithms......Page 88
Fourier transform of real images......Page 89
References......Page 91
Scale in signal processing......Page 92
Scale filters......Page 94
Windowed Fourier transform......Page 95
Gabor filter......Page 96
Local wave number......Page 99
Scale space and diffusion......Page 101
General properties of a scale space......Page 102
Linear scale spaces......Page 103
Differential scale spaces......Page 107
Discrete scale spaces......Page 108
Gaussian pyramid......Page 109
Laplacian pyramid......Page 111
Directio-pyramidal decomposition......Page 112
References......Page 115
Elementary Spatial Processing......Page 116
Neighborhood Operators......Page 118
Definition of neighborhood operators......Page 119
Shape and symmetry of neighborhoods......Page 120
Operator notation......Page 121
Linearity......Page 123
Point spread function......Page 124
Symmetries......Page 126
LSI operators as least squares estimators......Page 128
Transfer function and z-transform......Page 131
Relation between recursive and nonrecursive filters......Page 133
Zero-phase recursive filtering......Page 134
Basic recursive filters......Page 135
Limitations of linear filters......Page 138
Rank-value filters......Page 139
Adaptive and steerable filters......Page 140
Efficient neighborhood operations......Page 141
Minimizing computational effort......Page 142
Efficient storage schemes......Page 144
Neighborhood operators at borders......Page 147
References......Page 148
Introduction......Page 150
Classical design criteria in signal processing......Page 151
Filter design criteria for computer vision......Page 152
Windowing techniques......Page 153
Filter cascading......Page 157
Filter design as an optimization problem......Page 158
Parameterized ansatz......Page 159
Reference function......Page 161
Error functional......Page 162
Solution strategies......Page 163
Examples......Page 164
Design of steerable filters and filter families......Page 167
Gradient computation......Page 169
Optimization of filter families......Page 170
References......Page 176
Introduction......Page 178
General properties of transfer functions......Page 179
Symmetry and isotropy......Page 180
Separable averaging filters......Page 182
Type I box filters......Page 183
Type II box filters......Page 186
Box filters on hexagonal lattices......Page 187
General properties......Page 188
Binomial filters on square lattices......Page 189
Binomial filters on hexagonal lattices......Page 191
Multistep averaging......Page 192
Multigrid averaging......Page 197
Weighted averaging......Page 198
References......Page 199
Introduction......Page 200
Interpolation as convolution......Page 201
Interpolation on orthogonal lattices......Page 202
General properties of interpolation kernels......Page 203
Interpolation in Fourier space......Page 205
Linear interpolation......Page 207
Higher-order polynomial interpolation......Page 209
Spline-based interpolation......Page 211
Optimized interpolation......Page 215
References......Page 217
Introduction......Page 218
Forward and inverse mapping......Page 219
Affine transform......Page 220
Perspective transform......Page 221
Transforms defined by point correspondences......Page 222
Transforms defined by displacement vector fields......Page 223
Fast algorithms for geometric transforms......Page 224
Scaling......Page 225
Translation......Page 226
Rotation......Page 227
Affine and perspective transforms......Page 230
References......Page 231
Feature Estimation......Page 232
Local Structure......Page 234
Representation in the spatial domain......Page 235
Representation in the Fourier domain......Page 236
Direction versus orientation......Page 237
Edge detection by first-order derivatives......Page 238
General properties......Page 239
First-order difference operators......Page 240
Roberts operator......Page 242
Regularized difference operators......Page 243
Spline-based difference operators......Page 245
Least squares optimized gradient......Page 246
General properties......Page 248
Laplace of Gaussian and difference of Gaussian filters......Page 249
Edges in multichannel images......Page 251
Introduction......Page 252
The structure tensor......Page 253
Classification of local neighborhoods......Page 255
The inertia tensor......Page 256
Computation of the structure tensor......Page 259
Orientation vector......Page 260
Coherency......Page 261
Color coding of the two-dimensional structure tensor......Page 262
References......Page 263
Principles for Automatic Scale Selection......Page 264
Scale-space representation......Page 265
Gaussian and directional derivative operators......Page 266
Differential invariants......Page 267
Windowed spectral moment descriptors......Page 269
The need for automatic scale selection......Page 270
Normalized derivatives......Page 272
Properties of the scale-selection principle......Page 274
Interpretation of normalized derivatives......Page 275
Edge detection......Page 276
Ridge detection......Page 280
Blob detection......Page 282
Corner detection......Page 284
Local frequency estimation......Page 285
Corner localization......Page 287
Scale-selection principle for feature localization......Page 288
Stereo matching with automatic scale selection......Page 289
Scale-selection principle for estimating image deformations......Page 290
Properties of matching with automatic scale selection......Page 292
Summary and conclusions......Page 294
References......Page 295
Texture Analysis......Page 300
Texture analysis in machine vision......Page 301
Haralick\'s gray-level co-occurrence features......Page 303
Unser\'s sum and difference histograms......Page 307
Galloway\'s run-length-based features......Page 308
Chen\'s geometric features......Page 309
Laine\'s textural energy from Daubechies wavelets......Page 311
Local textural features......Page 312
Fractal features......Page 314
Laws filter masks for textural energy......Page 316
Fourier features......Page 317
Texture analysis from pyramid decomposition......Page 318
Markov random field approach......Page 319
Autoregressive models......Page 320
Assessment of textural features......Page 323
Setup and criteria......Page 324
Data sets for benchmarking......Page 325
Experiments and results......Page 328
Automatic design of texture analysis systems......Page 331
References......Page 332
Motion......Page 334
Introduction......Page 335
Optical flow......Page 337
Physical and visual correspondence......Page 344
Flow versus correspondence......Page 345
Differential techniques......Page 346
Tensor-based techniques......Page 353
Multifeature-based techniques......Page 366
Accurate and efficient implementation......Page 369
Quadrature filter techniques......Page 370
Spatiotemporal energy models......Page 371
Structure tensor from quadrature filter sets......Page 374
Phase techniques......Page 376
Correlation and matching......Page 378
Cross correlation......Page 379
Distance minimization matching......Page 380
Modeling of flow fields......Page 381
Parameterization of flow fields......Page 382
Robust estimates......Page 390
General properties......Page 394
Interrelation of common confidence measures......Page 396
Comparative analysis......Page 398
Test data......Page 399
Error measures......Page 402
Comparison of methods and parameters......Page 405
Results from generated synthetic data......Page 406
Results from realistic textures......Page 409
Summary......Page 416
References......Page 417
Introduction......Page 422
Differential formulation......Page 423
Uncertainty model......Page 425
Coarse-to-fine estimation......Page 429
Derivative filter kernels......Page 435
Multiscale warping......Page 437
Boundary handling......Page 438
Performance measures......Page 439
Synthetic sequences......Page 440
Conclusion......Page 444
References......Page 445
Nonlinear Diffusion Filtering......Page 448
Introduction......Page 449
Limitations of linear diffusion filtering......Page 450
Isotropic nonlinear diffusion......Page 452
Edge-enhancing anisotropic diffusion......Page 456
Coherence-enhancing anisotropic diffusion......Page 457
Continuous theory......Page 458
Regularized isotropic diffusion......Page 461
Anisotropic nonlinear diffusion......Page 463
Discrete theory......Page 464
Parameter selection......Page 466
Vector-valued models......Page 469
Summary......Page 470
References......Page 471
Introduction......Page 476
Motivation and general problem formulation......Page 477
Basic references to the literature......Page 478
Processing of two- and three-dimensional images......Page 480
Variational principle......Page 481
Finite element method discretization......Page 484
Algorithm......Page 491
Applications......Page 493
Processing of vector-valued images......Page 496
Variational principle......Page 497
Finite element method discretization......Page 499
Numerical example: color images......Page 500
Variational principle......Page 501
Finite element method discretization......Page 502
Numerical examples......Page 504
References......Page 506
Introduction......Page 510
Stereo geometry......Page 512
Hering coordinates......Page 513
Horizontal disparity......Page 515
Vertical disparity and epipolar lines......Page 517
Binocular camera movements......Page 519
The space horopter......Page 521
Stereo camera heads......Page 522
Global disparity......Page 524
Inverse perspective mapping......Page 525
References......Page 527
Introduction......Page 530
Intensity-based stereo: basic features......Page 532
Global versus local optimization......Page 533
Statistical decisions in terrain reconstruction......Page 534
Symmetric stereo geometry......Page 535
Simple and compound Bayesian decisions......Page 537
Prior geometric model......Page 539
Prior photometric models......Page 541
Posterior model of a profile......Page 543
Unified dynamic programming framework......Page 545
Regularizing heuristics......Page 546
Confidence of the digital parallax map......Page 548
Experimental results......Page 549
References......Page 553
Reflectance-Based Shape Recovery......Page 556
Introduction......Page 557
Shape from shading and photometric stereo......Page 558
Linear sensor......Page 560
Illumination parameters......Page 563
Reflectance distribution functions and maps......Page 564
Reflection and image irradiance equation......Page 570
Depth maps from gradient maps......Page 574
Albedo-dependent analysis......Page 577
Albedo-independent analysis......Page 580
Two light sources......Page 583
Albedo-dependent analysis......Page 584
Albedo-independent analysis......Page 595
Theoretical framework for shape from shading......Page 596
Shape from shading......Page 599
Images without solution......Page 600
Ambiguous shading patterns......Page 601
Method of characteristic strips......Page 602
Method of equal-height contours......Page 606
Direct variational method......Page 608
Concluding remarks......Page 611
References......Page 612
Depth-from-Focus......Page 616
Basic concepts......Page 617
Defocused imaging......Page 618
Principles of depth-from-focus algorithms......Page 620
Multiple-view depth-from-focus......Page 621
Sharpness measure......Page 622
Three-dimensional reconstruction......Page 625
Dual aperture......Page 626
Dual aperture and focus......Page 628
Sharp discontinuities......Page 633
Object-based depth-from-focus......Page 638
References......Page 647
Object Analysis, Classification, Modeling, Visualization......Page 650
Morphological Operators......Page 652
Introduction......Page 653
Image transforms and cross sections......Page 654
Order relationships......Page 656
Graph, path, and connectivity......Page 657
Discrete distances and distance functions......Page 658
Image operator properties......Page 659
Structuring element......Page 661
Erosion and dilation......Page 662
Morphological gradients......Page 665
Opening and closing......Page 667
Granulometries......Page 671
Geodesic operators......Page 673
Reconstruction-based operators......Page 676
Hit-or-miss......Page 681
Thinning and Thickening......Page 683
Distance transforms......Page 684
Erosions and dilations......Page 685
Openings and granulometries......Page 687
Geodesic transforms......Page 688
Correction of uneven illumination......Page 689
An erosion-based image measurement......Page 690
Filtering......Page 691
Segmentation......Page 699
References......Page 703
Fuzzy Image Processing......Page 708
Introduction......Page 709
A brief history......Page 710
Basics of fuzzy set theory......Page 711
Fuzzy logic versus probability theory......Page 715
Framework for knowledge representation/processing......Page 716
A new image definition: Images as fuzzy sets......Page 717
Image fuzzification: From images to memberships......Page 718
Fuzzy topology......Page 721
Fuzzy image processing systems......Page 724
Operations in membership plane......Page 725
Fuzzy geometry......Page 727
Measures of fuzziness and image information......Page 730
Rule-based systems......Page 731
Fuzzy/possibilistic clustering......Page 733
Fuzzy morphology......Page 734
Fuzzy measure theory......Page 735
Image enhancement: contrast adaptation......Page 739
Edge detection......Page 741
Image segmentation......Page 743
Conclusions......Page 745
References......Page 747
Introduction......Page 754
Multilayer perceptron (MLP)......Page 755
Backpropagation-type neural networks......Page 757
Convolution neural networks (CNN)......Page 759
Kohonen maps......Page 761
Learning vector quantization......Page 764
Regularization networks......Page 765
Transformation radial-basis networks (TRBNN)......Page 768
Basic architecture considerations......Page 772
Modified Hopfield network......Page 774
References......Page 776
Graph Theoretical Concepts for Computer Vision......Page 778
Graphs, vertices, edges......Page 779
Paths, subgraphs, and components of a graph......Page 781
Circuits, cutsets, cuts, and dual graphs......Page 782
Planar graphs and geometrical duals......Page 783
Digital images......Page 785
The representation of the image......Page 786
Voronoi diagrams and Delaunay graphs......Page 787
Approaches for the computation of Voronoi diagrams......Page 798
Applications......Page 799
Matching......Page 800
Graph isomorphisms and matchings......Page 801
Matching in computer vision: problem statement......Page 803
Matching by association graph construction......Page 804
Graph......Page 805
Transformation rules......Page 807
References......Page 811
Introduction......Page 816
Incremental approach......Page 819
Three-dimensional shape reconstruction from contour lines......Page 822
Topological prerequisites......Page 823
Classification of tetrahedra......Page 824
Generalization for hierarchical contours......Page 825
Multiple cross sections......Page 826
Volumetric shape reconstruction......Page 827
Geometrical model......Page 828
Split-and-merge......Page 830
Segmentation and measurements......Page 832
Summary......Page 836
References......Page 838
Introduction......Page 842
Why probabilistic models?......Page 844
Object recognition: classification and regression......Page 846
Parametric families of model densities......Page 851
Histograms......Page 852
Probabilistic modeling of intensities and image points......Page 853
Model densities using geometric features......Page 859
Markov random fields......Page 862
Automatic model generation......Page 869
Parameter estimation......Page 870
Automatic learning of model structure......Page 874
Practical issues......Page 875
Summary, conclusions, and discussion......Page 876
References......Page 877
General remarks......Page 880
Overview of the approach......Page 882
Definition of a concept......Page 884
Instance and modified concept......Page 887
Function-centered representation......Page 888
Interpretation by optimization......Page 889
Control by graph search......Page 890
Control by combinatorial optimization......Page 893
Judgment function......Page 895
References......Page 897
Visualization of Volume Data......Page 900
The rendering equation......Page 901
Particle model approach......Page 903
Basic concepts and notation for visualization......Page 905
OpenGL......Page 906
Iso-surface extraction by marching cubes......Page 908
Ray-casting......Page 909
Shadowing approaches......Page 911
The graphics library VGL......Page 915
Volume primitives......Page 916
VGL rendering pipeline......Page 918
Clipping......Page 923
Classification......Page 924
Aliasing......Page 926
Classification......Page 927
Irregular grids......Page 928
Volume data sources......Page 929
References......Page 930
Databases for Microscopes and Microscopical Images......Page 932
Introduction......Page 933
Benefits......Page 934
From flat files to database systems......Page 936
Component specifications......Page 937
Image acquisition parameters......Page 939
Workflow and specimen parameters......Page 940
High-level programming environment......Page 942
Data flow---how it looks in practice......Page 943
Scanning and saving......Page 945
BioImage database......Page 946
Object relational database management systems......Page 948
Conclusions: application to other fields?......Page 949
References......Page 950
Index......Page 952