Digital Image Interpolation in Matlab

Chi-Wah Kok, Canaan Semiconductor Limited, Hong Kong, China Wing-Shan Tam, Canaan Semiconductor Limited, Hong Kong, China

About the Authors xiii

Preface xv

Acknowledgments xix

Nomenclature xxi

Abbreviations xxiii

About the CompanionWebsite xxv

1 Signal Sampling 1

1.1 Sampling and Bandlimited Signal 1

1.2 Unitary Transform 4

1.2.1 Discrete Fourier Transform 4

1.3 Quantization 5

1.3.1 Quantization and Sampling Interaction 7

1.4 Sampled Function Approximation: Fitting and Interpolation 8

1.4.1 Zero-Order Hold (ZOH) 10

1.4.2 First-Order Hold (FOH) 10

1.4.3 Digital Interpolation 12

1.5 Book Organization 12

1.6 Exercises 15

2 Digital Image 17

2.1 Digital Imaging in MATLAB 21

2.2 Current Pixel and Neighboring Pixels 23

2.3 Frequency Domain 24

2.3.1 Transform Kernel 28

2.4 2D Filtering 28

2.4.1 Boundary Extension and Cropping 30

2.4.1.1 Constant Extension 31

2.4.1.2 Periodic Extension 31

2.4.1.3 Symmetric Extension 32

2.4.1.4 Infinite Extension 32

2.4.1.5 Cropping 33

2.5 Edge Extraction 34

2.5.1 First-Order Derivative Edge Detection Operators 36

2.5.1.1 Sobel Operator 37

2.5.2 Second-Order Derivative and Zero-Crossing Edge Detector 40

2.5.2.1 Laplacian Operator 41

2.5.2.2 Gaussian Smoothing 42

2.6 Geometric Transformation 45

2.6.1 Translation 46

2.6.2 Reflection 47

2.6.3 Scaling 47

2.6.4 Rotation 49

2.6.5 Affine Transformation 50

2.7 Resize an Image 51

2.7.1 Interpolation 51

2.7.2 Decimation 54

2.7.2.1 Direct Subsampling 55

2.7.2.2 Sinc Filter 55

2.7.2.3 Block Averaging 56

2.7.3 Built-in Image Resizing Function in MATLAB 57

2.8 Color Image 58

2.8.1 Color Filter Array and Demosaicing 60

2.8.2 Perceptual Color Space 60

2.9 Noise 62

2.9.1 Rank Order Filtering 65

2.9.2 Smoothing Filtering 65

2.10 Summary 67

2.11 Exercises 67

3 Image Quality 71

3.1 Image Features and Artifacts 72

3.1.1 Aliasing (Jaggy) 73

3.1.2 Smoothing (Blurring) 74

3.1.3 Edge Halo 74

3.1.4 Ringing 75

3.1.5 Blocking 75

3.2 Objective Quality Measure 75

3.2.1 Mean Squares Error 77

3.2.2 Peak Signal-to-Noise Ratio 78

3.2.3 Edge PSNR 79

3.3 Structural Similarity 81

3.3.1 Luminance 83

3.3.2 Contrast 84

3.3.3 Structural 84

3.3.4 Sensitivity of SSIM 85

3.3.4.1 K1 Sensitivity 85

3.3.4.2 K2 Sensitivity 86

3.4 Summary 88

3.5 Exercises 88

4 Nonadaptive Interpolation 91

4.1 Image Interpolation: Overture 92

4.1.1 Interpolation Kernel Characteristics 94

4.1.2 Nearest Neighbor 94

4.1.3 Bilinear 98

4.1.4 Bicubic 103

4.2 Frequency Domain Analysis 110

4.3 Mystery of Order 111

4.4 Application: Affine Transformation 113

4.4.1 Structural Integrity 116

4.5 Summary 118

4.6 Exercises 120

5 Transform Domain 123

5.1 DFT Zero Padding Interpolation 125

5.1.1 Implementation 127

5.2 Discrete Cosine Transform 132

5.2.1 DCT Zero Padding Interpolation 134

5.3 DCT Zero Padding Image Interpolation 138

5.3.1 Blocked Transform 138

5.3.2 Block-Based DCT Zero Padding Interpolation 140

5.3.2.1 Does Kernel Size Matter 142

5.4 Overlapping 144

5.5 Multi-Kernels 149

5.5.1 Extendible Inverse DCT 149

5.6 Iterative Error Correction 152

5.7 Summary 156

5.8 Exercises 157

6 Wavelet 161

6.1 Wavelet Analysis 162

6.1.1 Perfect Reconstruction 163

6.1.2 Multi-resolution Analysis 164

6.1.3 2DWavelet Transform 166

6.2 Wavelet Image Interpolation 168

6.2.1 Zero Padding 168

6.2.2 Multi-resolution Subband Image Estimation 170

6.2.3 Hölder Regularity 176

6.2.3.1 Local Regularity-Preserving Problems 177

6.3 Cycle Spinning 179

6.3.1 Zero Padding (WZP-CS) 179

6.3.2 High Frequency Subband Estimation (WLR-CS) 181

6.4 Error Correction 184

6.5 WhichWavelets to Use 186

6.6 Summary 187

6.7 Exercises 188

7 Edge-Directed Interpolation 191

7.1 Explicit Edge-Directed Interpolation 193

7.2 Implicit Edge-Directed Interpolation 196

7.2.1 Canny Edge Interpolation (CEI) 197

7.2.2 Edge-Based Line Averaging (ELA) 198

7.2.3 Directional-Orientation Interpolation (DOI) 199

7.2.4 Error-Amended Sharp Edge (EASE) 201

7.3 Summary 208

7.4 Exercises 209

8 Covariance-Based Interpolation 211

8.1 Modeling of Image Features 212

8.2 Interpolation by Autoregression 213

8.3 New Edge-Directed Interpolation (NEDI) 215

8.3.1 Type 0 Estimation 220

8.3.2 Type 1 Estimation 222

8.3.3 Type 2 Estimation 223

8.3.4 Pixel Intensity Correction 225

8.3.5 MATLAB Implementation 226

8.4 Boundary Extension 228

8.5 Threshold Selection 231

8.6 Error PropagationMitigation 233

8.7 CovarianceWindow Adaptation 238

8.7.1 PredictionWindow Adaptation 239

8.7.2 Mean CovarianceWindow Adaptation 241

8.7.3 Enhanced Modified Edge-Directed Interpolation (EMEDI) 242

8.8 Iterative Covariance Correction 249

8.8.1 iMEDI Implementation 255

8.9 Summary 260

8.10 Exercises 261

9 Partitioned Fractal Interpolation 263

9.1 Iterated Function System 264

9.1.1 Banach Fixed-Point Theorem 264

9.2 Partitioned Iterative Function System 266

9.3 Encoding 269

9.3.1 Range Block Partition 269

9.3.2 Domain Block Partition 270

9.3.3 Codebook Generation 271

9.3.4 Grayscale Scaling 274

9.3.5 Fractal Encoding Implementation 276

9.4 Decoding 277

9.4.1 Does Size Matter 281

9.5 Decoding with Interpolation 283

9.5.1 From Fitting to Interpolation 285

9.6 Overlapping 287

9.7 Summary 289

9.8 Exercises 290

Appendix MATLAB Functions List 291

Bibliography 295

Index 299