Digital Image Processing (eBook)

Preface 5
Contents 9
Part I Foundation 14
1 Applications and Tools 16
1.1 A Tool for Science and Technique 16
1.2 Examples of Applications 17
1.3 Hierarchy of Image Processing Operations 28
1.4 Image Processing and Computer Graphics 30
1.5 Cross-disciplinary Nature of Image Processing 30
1.6 Human and Computer Vision 31
1.7 Components of an Image Processing System 34
1.8 Exercises 39
1.9 Further Readings 41
2 Image Representation 44
2.1 Introduction 44
2.2 Spatial Representation of Digital Images 44
2.3 Wave Number Space and Fourier Transform 54
2.4 Discrete Unitary Transforms 76
2.5 Fast Algorithms for Unitary Transforms 80
2.6 Exercises 90
2.7 Further Readings 93
3 Random Variables and Fields 94
3.1 Introduction 94
3.2 Random Variables 96
3.3 Multiple Random Variables 100
3.4 Probability Density Functions 104
3.5 Stochastic Processes and Random Fields 111
3.6 Exercises 115
3.7 Further Readings 117
4 Neighborhood Operations 118
4.1 Basic Properties and Purpose 118
4.2 Linear Shift-Invariant Filters 121
4.3 Rank Value Filters 132
4.4 LSI-Filters: Further Properties 133
4.5 Recursive Filters 135
4.6 Recursive Filters 144
4.7 Further Readings 147
5 Multiscale Representation 148
5.1 Scale 148
5.2 Multigrid Representations 151
5.3 Scale Spaces 157
5.4 Exercises 165
5.5 Further Readings 166
Part II Image Formation and Preprocessing 168
6 Quantitative Visualization 170
6.1 Introduction 170
6.2 Radiometry, Photometry, Spectroscopy, and Color 172
6.3 Waves and Particles 181
6.4 Interactions of Radiation with Matter 187
6.5 Exercises 199
6.6 Further Readings 200
7 Image Formation 202
7.1 Introduction 202
7.2 World and Camera Coordinates 202
7.3 Ideal Imaging: Perspective Projection 205
7.4 Real Imaging 208
7.5 Radiometry of Imaging 214
7.6 Linear System Theory of Imaging 218
7.7 Homogeneous Coordinates 225
7.8 Exercises 227
7.9 Further Readings 228
8 3-D Imaging 230
8.1 Basics 230
8.2 Depth from Triangulation 234
8.3 Depth from Time-of-Flight 241
8.4 Depth from Phase: Interferometry 242
8.5 Shape from Shading 242
8.6 Depth from Multiple Projections: Tomography 248
8.7 Exercises 254
8.8 Further Readings 255
9 Digitization, Sampling, Quantization 256
9.1 Definition and E.ects of Digitization 256
9.2 Image Formation, Sampling, Windowing 258
9.3 Reconstruction from Samples 262
9.4 Multidimensional Sampling on Nonorthogonal Grits 264
9.5 Quantization 266
9.6 Exercises 267
9.7 Further Readings 268
10 Pixel Processing 270
10.1 Introduction 270
10.2 Homogeneous Point Operations 271
10.3 Inhomogeneous Point Operations 281
10.4 Geometric Transformations 288
10.5 Interpolation 292
10.6 Optimized Interpolation 299
10.7 Multichannel Point Operations 304
10.8 Exercises 306
10.9 Further Redings 308
Part III Feature Extraction 310
11 Averaging 312
11.1 Introduction 312
11.2 General Properties of Averaging Filters 312
11.3 Box Filter 315
11.4 Binomial Filter 319
11.5 Effcient Large-Scale Averaging 325
11.6 Nonlinear Averaging 334
11.7 Averaging in Multichannel Images 339
11.8 Exercises 341
11.9 Further Redings 343
12 Edges 344
12.1 Introduction 344
12.2 Differential Description of Signal Changes 345
12.3 General Properties of Edge Filters 348
12.4 Gradient-Based Edge Detection 351
12.5 Edge Detection by Zero Crossings 358
12.6 Optimized Edge Detection 360
12.7 Regularized Edge Detection 362
12.8 Edges in Multichannel Images 366
12.9 Exercises 368
12.10 Further Redings 370
13 Simple Neighborhoods 372
13.1 Introduction 372
13.2 Properties of Simple Neighborhoods 373
13.3 First-Order Tensor Representation 377
13.4 Local Wave Number and Phase 388
13.5 Further Tensor Representations 397
13.6 Exercises 408
13.7 Further Redings 409
14 Motion 410
14.1 Introduction 410
14.2 Basics 411
14.3 First-Order Di.erential Methods 426
14.4 Tensor Methods 431
14.5 Correlation Methods 436
14.6 Phase Method 439
14.7 Additional Methods 441
14.8 Exercises 447
14.9 Fruther Readings 447
15 Texture 448
15.1 Introduction 448
15.2 First-Order Statistics 451
15.3 Rotation and Scale Variant Texture Features 455
15.4 Exercises 459
15.5 Further Readings 459
Part IV Image Analysis 460
16 Segmentation 462
16.1 Introduction 462
16.2 Pixel-Based Segmentation 462
16.3 Edge-Based Segmentation 466
16.4 Region-Based Segmentation 467
16.5 Model-Based Segmentation 471
16.6 Exercises 474
16.7 Further Readings 475
17 Regularization and Modeling 476
17.1 Introduction 476
17.2 Continuous Modeling I: Veriational Approach 479
17.3 Continuous Modeling II: Diffusion 486
17.4 Discrete Modeling: Inverse Problems 491
17.5 Inverse Filtering 499
17.6 Further Equivalent Approaches 505
17.7 Exercises 511
17.8 Further Redings 513
18 Morphology 514
18.1 Introduction 514
18.2 Neighborhood Operations on Binary Images 514
18.3 General Properties 516
18.4 Composite Morphological Operators 519
18.5 Exercises 525
18.6 Furtheer Readings 527
19 Shape Presentation and Analysis 528
19.1 Introduction 528
19.2 Representation of Shape 528
19.3 Moment-Based Shape Features 533
19.4 Fourier Descriptors 535
19.5 Shape Parameters 541
19.6 Exercises 544
19.7 Further Readings 545
20 Classification 546
20.1 Introduction 546
20.2 Feature Space 549
20.3 Simple Classi.cation Techniques 556
20.4 Exercises 561
20.5 Further Readings 562
Part V Reference Part 564
A Reference Material 566
B Notation 590
Bibliography 598
Index 610

14 Motion (p. 397-398)


14.1 Introduction

Motion analysis long used to be a specialized research area that had not much to do with general image processing. This separation had two reasons. First, the techniques used to analyze motion in image sequences were quite different. Second, the large amount of storage space and computing power required to process image sequences made image sequence analysis available only to a few specialized institutions that could afford to buy the expensive specialized equipment.

Both reasons are no longer true. Because of the general progress in image processing, the more advanced methods used in motion analysis no longer differ from those used for other image processing tasks. The rapid progress in computer hardware and algorithms makes the analysis of image sequences now feasible even on standard personal computers and workstations.

Therefore we treat motion in this chapter as just another feature that can be used to identify, characterize, and distinguish objects and to understand scenes. Motion is indeed a powerful feature. We may compare the integration of motion analysis into mainstream image processing with the transition from still photography to motion pictures.

Only image sequence analysis allows us to recognize and analyze dynamic processes. Thus far-reaching capabilities become available for scientific and engineering applications including the study of flow; transport; biological growth processes from the molecular to the ecosystem level; diurnal, annual, and interannual variations; industrial processes; trafic; autonomous vehicles and robots - to name just a few application areas. In short, everything that causes temporal changes or makes them visible in our world is a potential subject for image sequence analysis.

The analysis of motion is still a challenging task and requires some special knowledge. Therefore we discuss the basic problems and principles of motion analysis in Section 14.2. Then we turn to the various techniques for motion determination. As in many other areas of image processing, the literature is swamped with a multitude of approaches. This book should not add to the confusion. We emphasize instead the basic principles and we try to present the various concepts in a unified way as filter operations on the space-time images.

In this way, the interrelations between the different concepts are made transparent. In this sense, we will discuss differential (Section 14.3), tensor (Section 14.4), correlation (Section 14.5), and phase (Section 14.6) techniques as elementary motion estimators.