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Digital image warping (IEEE Computer Society Press monograph), by George Wolberg
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This best-selling, original text focuses on image reconstruction, real-time texture mapping, separable algorithms, two-pass transforms, mesh warping, and special effects. The text, containing all original material, begins with the history of the field and continues with a review of common terminology, mathematical preliminaries, and digital image acquisition. Later chapters discuss equations for spatial information, interpolation kernels, filtering problems, and fast-warping techniques based on scanline algorithms.
- Sales Rank: #16902120 in Books
- Published on: 1992
- Binding: Unknown Binding
- 318 pages
Most helpful customer reviews
12 of 12 people found the following review helpful.
Classic reference, unfortunately out of print
By Jon A. Webb
George Wolberg invented the digital image warping techniques that were used to make the special effects in Willow and The Abyss. "Digital Image Warping" is the classic reference for fast image warping. It is the first place I went to learn how to speed up this operation. Unfortunately, this book is now out of print, but it is still available directly from the author. As the previous reviewer indicates, this is not a programming text; but it is clearly written and explores a wide variety of image warping techniques, clearly describing highly efficient algorithms for each. This book is without peer for this important class of image operations.
4 of 4 people found the following review helpful.
Good overview but lacking in practical details
By calvinnme
This book is a clearly written overview of the field and its algorithms, but it is not a good detailed practical guide. I am yet to find a paper or a book that talks about these methods clearly and then shares solutions to some examples. I'd say this book is an essential foundation in going further, but you'll still need to do some research and programming experiments of your own to understand the subject. I do take my hat off to Wolberg to being the only person to tackle this subject in print and do an even half-way adequate job of it.
Chapter 1 discusses the history of this field and presents a brief overview of the other chapters. A review of common terminology, mathematical preliminaries, and digital image acquisition is presented in Chapter 2. As we shall see later, digital image warping consists of two basic operations: a spatial transformation to define the rearrangement of pixels and interpolation to compute their values. Don't judge the book too harshly by these first two chapters. Most books on image processing topics have overview chapters that are not that helpful because they are too general.
Chapter three is where the specifics come into play. It describes various common methods for spatial transformations, as well as techniques for inferring them when only a set of correspondence points are known. Chapter 4 provides a review of sampling theory, which is the mathematical framework used to describe the filtering problems that follow. Chapter 5 describes image resampling, including several common interpolation kernels. These are used in the discussion of antialiasing in Chapter 6. This chapter demonstrates several approaches used to avoid artifacts that manifest themselves to the discrete nature of digital images. Fast warping techniques based on scanline algorithms are presented in Chapter 7. These results are particularly useful for both hardware and software realizations of geometric transformations. Finally, the main points of the book are basically repeated in Chapter 8. Source code, written in C, is scattered among the chapters and appendices to demonstrate implementation details for various algorithms.
The problem with the book is that the algorithms are clear enough, what is not clear is how one would use all of this to correct imagery and under what circumstances. In short, the author either gives a broad overview or a minute derivation of the math with some code. What would have been nice would have been some extended examples to tie it all together. The following is the table of contents, listed because it is currently not part of the product description.
CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND 1
1.2 OVERVIEW 6
1.2.1 Spatial Transformations 6
1.2.2 Sampling Theory 7
1.2.3 Resampling 7
1.2.4 Aliasing 8
1.2.5 Scanline Algorithms 9
1.3 CONCEPTUAL LAYOUT 10
CHAPTER 2 PRELIMINARIES 11
2.1 FUNDAMENTALS 11
2.1.1 Signals and Images 11
2.1.2 Filters 14
2.1.3 Impulse Response 15
2.1.4 Convolution 16
2.1.5 Frequency Analysis 19
2.1.5.1 An Analogy to Audio Signals 19
2.1.5.2 Fourier Transforms 20
2.1.5.3 Discrete Fourier Transforms 26
2.2 IMAGE ACQUISITION 28
2.3 IMAGING SYSTEMS 32
2.3.1 Electronic Scanners 32
2.3.1.1 Vidicon Systems 33
2.3.1.2 Image Dissectors 34
2.3.2 Solid-State Sensors 35
2.3.2.1 CCD Cameras 35
2.3.2.2 CID Cameras 36
2.3.3 Mechanical Scanners 36
2.4 VIDEO DIGITIZERS 37
2.5 DIGITIZED IMAGERY 38
2.6 SUMMARY 40
CHAPTER 3 SPATIAL TRANSFORMATIONS 41
3.1 DEFINITIONS 42
3.1.1 Forward Mapping 42
3.1.2 Inverse Mapping 44
3.2 GENERAL TRANSFORMATION MATRIX 45
3.2.1 Homogeneous Coordinates 46
3.3 AFFINE TRANSFORMATIONS 47
3.3.1 Translation 48
3.3.2 Rotation 49
3.3.3 Scale 49
3.3.4 Shear 49
3.3.5 Composite Transformations 50
3.3.6 Inverse 50
3.3.7 Inferring Affine Transformations 50
3.4 PERSPECTIVE TRANSFORMATIONS 52
3.4.1 Inverse 52
3.4.2 Inferring Perspective Transformations 53
3.4.2.1 Case 1: Square-to-Quadrilateral 54
3.4.2.2 Case 2: Quadrilateral-to-Square 56
3.4.2.3 Case 3: Quadrilateral-to-Quadrilateral56
3.5 BILINEAR TRANSFORMATIONS 57
3.5.1 Bilinear Interpolation 58
3.5.2 Separability 59
3.5.3 Inverse 60
3.5.4 Interpolation Grid 60
3.6 POLYNOMIAL TRANSFORMATIONS 61
3.6.1 Inferring Polynomial Coefficients 63
3.6.2 Pseudoinverse Solution 64
3.6.3 Least-Squares With Ordinary Polynomials 65
3.6.4 Least-Squares With Orthogonal Polynomials 67
3.6.5 Weighted Least-Squares 70
3.7 PIECEWISE POLYNOMIAL TRANSFORMATIONS 75
3.7.1 A Surface Fitting Paradigm for Geometric Correction 75
3.7.2 Procedure 77
3.7.3 Triangulation 78
3.7.4 Linear Triangular Patches 78
3.7.5 Cubic Triangular Patches 80
3.8 GLOBAL SPLINES 81
3.8.1 Basis Functions 81
3.8.2 Regularization 84
3.8.2.1 Grimson, 1981 85
3.8.2.2 Terzopoulos, 1984 86
3.8.2.3 Discontinuity Detection 87
3.8.2.4 Boult and Kender, 1986 88
3.8.2.5 A Definition of Smoothness 91
3.9 SUMMARY 92
CHAPTER 4 SAMPLING THEORY 95
4.1 INTRODUCTION 95
4.2 SAMPLING 96
4.3 RECONSTRUCTION 99
4.3.1 Reconstruction Conditions 99
4.3.2 Ideal Low-Pass Filter 100
4.3.3 Sinc Function 101
4.4 NONIDEAL RECONSTRUCTION 103
4.5 ALIASING 106
4.6 ANTIALIASING 108
4.7 SUMMARY 112
CHAPTER 5 IMAGE RESAMPLING 117
5.1 INTRODUCTION 117
5.2 IDEAL IMAGE RESAMPLING 119
5.3 INTERPOLATION 124
5.4 INTERPOLATION KERNELS 126
5.4.1 Nearest Neighbor 126
5.4.2 Linear Interpolation 127
5.4.3 Cubic Convolution 129
5.4.4 Two-Parameter Cubic Filters 131
5.4.5 Cubic Splines 133
5.4.5.1 B-Splines 134
5.4.5.2 Interpolating B-Splines 136
5.4.6 Windowed Sinc Function 137
5.4.6.1 Hann and Hamming Windows 139
5.4.6.2 Blackman Window 140
5.4.6.3 Kaiser Window 141
5.4.6.4 Lanczos Window 142
5.4.6.5 Gaussian Window 143
5.4.7 Exponential Filters 145
5.5 COMPARISON OF INTERPOLATION METHODS 147
5.6 IMPLEMENTATION 150
5.6.1 Interpolation with Coefficient Bins 150
5.6.2 Fant's Resampling Algorithm 153
5.7 DISCUSSION 160
CHAPTER 6 ANTIALIASING 163
6.1 INTRODUCTION 163
6.1.1 Point Sampling 163
6.1.2 Area Sampling 166
6.1.3 Space-Invariant Filtering 168
6.1.4 Space-Variant Filtering 168
6.2 REGULAR SAMPLING 168
6.2.1 Supersampling 168
6.2.2 Adaptive Supersampling 169
6.2.3 Reconstruction from Regular Samples 171
6.3 IRREGULAR SAMPLING 173
6.3.1 Stochastic Sampling 173
6.3.2 Poisson Sampling 174
6.3.3 Jittered Sampling 175
6.3.4 Point-Diffusion Sampling 176
6.3.5 Adaptive Stochastic Sampling 177
6.3.6 Reconstruction from Irregular Samples 177
6.4 DIRECT CONVOLUTION 178
6.4.1 Catmull, 1974 178
6.4.2 Blinn and Newell, 1976 178
6.4.3 Feibush, Levoy, and Cook, 1980 178
6.4.4 Gangnet, Perny, and Coueignoux, 1982 179
6.4.5 Greene and Heckbert, 1986 179
6.5 PREFILTERING 181
6.5.1 Pyramids 181
6.5.2 Summed-Area Tables 183
6.6 FREQUENCY CLAMPING 184
6.7 ANTIALIASED LINES AND TEXT 184
6.8 DISCUSSION 185
CHAPTER 7 SCANLINE ALGORITHMS 187
7.1 INTRODUCTION 188
7.1.1 Forward Mapping 188
7.1.2 Inverse Mapping 188
7.1.3 Separable Mapping 188
7.2 INCREMENTAL ALGORITHMS 189
7.2.1 Texture Mapping 189
7.2.2 Gouraud Shading 190
7.2.3 Incremental Texture Mapping 191
7.2.4 Incremental Perspective Transformations 196
7.2.5 Approximation 197
7.2.6 Quadratic Interpolation 199
7.2.7 Cubic Interpolation 201
7.3 ROTATION 205
7.3.1 Braccini and Marino, 1980 205
7.3.2 Weiman, 1980 206
7.3.3 Catmull and Smith, 1980 206
7.3.4 Paeth, 1986/ Tanaka, et. al., 1986 208
7.3.5 Cordic Algorithm 212
7.4 2-PASS TRANSFORMS 214
7.4.1 Catmull and Smith, 1980 215
7.4.1.1 First Pass 215
7.4.1.2 Second Pass 215
7.4.1.3 2-Pass Algorithm 217
7.4.1.4 An Example: Rotation 217
7.4.1.5 Another Example: Perspective 218
7.4.1.6 Bottleneck Problem 219
7.4.1.7 Foldover Problem 220
7.4.2 Fraser, Schowengerdt, and Briggs, 1985 221
7.3.3 Smith, 1987 221
7.5 2-PASS MESH WARPING 222
7.5.1 Special Effects 222
7.5.2 Description of the Algorithm 224
7.5.2.1 First Pass 225
7.5.2.2 Second Pass 228
7.5.2.3 Discussion 228
7.5.3 Examples 230
7.5.4 Source Code 233
7.6 MORE SEPARABLE MAPPINGS 240
7.6.1 Perspective Projection: Robertson, 1987 240
7.6.2 Warping Among Arbitrary Planar Shapes:
Wolberg, 1988 241
7.6.3 Spatial Lookup Tables:
Wolberg and Boult, 1989 242
7.7 SEPARABLE IMAGE WARPING 242
7.7.1 Spatial Lookup Tables 244
7.7.2 Intensity Resampling 244
7.7.3 Coordinate Resampling 245
7.7.4 Distortions and Errors 245
7.7.4.1 Filtering Errors 246
7.7.4.2 Shear 246
7.7.4.3 Perspective 248
7.7.4.4 Rotation 248
7.7.4.5 Distortion Measures 248
7.7.4.6 Bottleneck Distortion 250
7.7.5 Foldover Problem 251
7.7.5.1 Representing Foldovers 251
7.7.5.2 Tracking Foldovers 252
7.7.5.3 Storing Information From Foldovers 253
7.7.5.4 Intensity Resampling with Foldovers 254
7.7.6 Compositor 254
7.7.7 Examples 254
7.8 DISCUSSION 260
CHAPTER 8 EPILOGUE 261
APPENDIX 1 FAST FOURIER TRANSFORMS 265
A1.1 DISCRETE FOURIER TRANSFORM 266
A1.2 DANIELSON-LANCZOS LEMMA 267
A1.2.1 Butterfly Flow Graph 269
A1.2.2 Putting It All Together 270
A1.2.3 Recursive FFT Algorithm 272
A1.2.4 Cost of Computation 273
A1.3 COOLEY-TUKEY ALGORITHM 274
A1.3.1 Computational Cost 275
A1.4 COOLEY-SANDE ALGORITHM 276
A1.5 SOURCE CODE 278
A1.5.1 Recursive FFT Algorithm 279
A1.5.2 Cooley-Tukey FFT Algorithm 281
APPENDIX 2 INTERPOLATING CUBIC SPLINES 283
A2.1 DEFINITION 283
A2.2 CONSTRAINTS 284
A2.3 SOLVING FOR THE SPLINE COEFFICIENTS 285
A2.3.1 Derivation of A_2 285
A2.3.2 Derivation of A_3 286
A2.3.3 Derivation of A_1 and A_3 286
A2.4 EVALUTING THE UNKNOWN DERIVATIVES 287
A2.4.1 First Derivatives 287
A2.4.2 Second Derivatives 288
A2.4.3 Boundary Conditions 289
A2.5 SOURCE CODE 290
A2.5.1 Ispline 290
A2.5.2 Ispline_gen 293
APPENDIX 3 FORWARD DIFFERENCE METHOD 297
REFERENCES 301
INDEX 315
2 of 2 people found the following review helpful.
Good general overview
By Thad Beier
I read Wolberg's book after writing my own morph program, I wish I had read it beforehand. It gives a good overview of warping techniques, clearly differentiates between forward and inverse mapping, and gives by far the best description of Doug Smythe's morphing program that exists.
People who complain about a lack of code samples are whiners. Nothing in this book is complex in the least, and the implementation of any of the algorithms in it is pretty straightforward.
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