Part I Overview

1 Introduction 3

1.1 Real Threat or Hype? 3

1.2 Artificial Intelligence and Learning 4

1.3 How to Read this Book 5

2 Steganography and Steganalysis 7

2.1 Cryptography versus Steganography 7

2.2 Steganography 8

2.2.1 The Prisoners’ Problem 9

2.2.2 Covers – Synthesis and Modification 10

2.2.3 Keys and Kerckhoffs’ Principle 12

2.2.4 LSB Embedding 13

2.2.5 Steganography and Watermarking 15

2.2.6 Different Media Types 16

2.3 Steganalysis 17

2.3.1 The Objective of Steganalysis 17

2.3.2 Blind and Targeted Steganalysis 18

2.3.3 Main Approaches to Steganalysis 19

2.3.4 Example: Pairs of Values 22

2.4 Summary and Notes 23

3 Getting Started with a Classifier 25

3.1 Classification 25

3.1.1 Learning Classifiers 26

3.1.2 Accuracy 27

3.2 Estimation and Confidence 28

3.3 Using libSVM 30

3.3.1 Training and Testing 30

3.3.2 Grid Search and Cross-validation 31

3.4 Using Python 33

3.4.1 Why we use Python 33

3.4.2 Getting Started with Python 34

3.4.3 Scientific Computing 35

3.4.4 Python Imaging Library 36

3.4.5 An Example: Image Histogram 37

3.5 Images for Testing 38

3.6 Further Reading 39

Part II Features

4 Histogram Analysis 43

4.1 Early Histogram Analysis 43

4.2 Notation 44

4.3 Additive Independent Noise 44

4.3.1 The Effect of Noise 45

4.3.2 The Histogram Characteristic Function 47

4.3.3 Moments of the Characteristic Function 48

4.3.4 Amplitude of Local Extrema 51

4.4 Multi-dimensional Histograms 54

4.4.1 HCF Features for Colour Images 55

4.4.2 The Co-occurrence Matrix 57

4.5 Experiment and Comparison 63

5 Bit-plane Analysis 65

5.1 Visual Steganalysis 65

5.2 Autocorrelation Features 67

5.3 Binary Similarity Measures 69

5.4 Evaluation and Comparison 72

6 More Spatial Domain Features 75

6.1 The Difference Matrix 75

6.1.1 The EM Features of Chen et al. 76

6.1.2 Markov Models and the SPAM Features 79

6.1.3 Higher-order Differences 81

6.1.4 Run-length Analysis 81

6.2 Image Quality Measures 82

6.3 Colour Images 86

6.4 Experiment and Comparison 86

7 The Wavelets Domain 89

7.1 A Visual View 89

7.2 The Wavelet Domain 90

7.2.1 The Fast Wavelet Transform 91

7.2.2 Example: The Haar Wavelet 92

7.2.3 The Wavelet Transform in Python 93

7.2.4 Other Wavelet Transforms 94

7.3 Farid’s Features 96

7.3.1 The Image Statistics 96

7.3.2 The Linear Predictor 96

7.3.3 Notes 98

7.4 HCF in the Wavelet Domain 98

7.4.1 Notes and Further Reading 100

7.5 Denoising and the WAM Features 101

7.5.1 The Denoising Algorithm 101

7.5.2 Locally Adaptive LAW-ML 103

7.5.3 Wavelet Absolute Moments 104

7.6 Experiment and Comparison 106

8 Steganalysis in the JPEG Domain 107

8.1 JPEG Compression 107

8.1.1 The Compression 108

8.1.2 Programming JPEG Steganography 110

8.1.3 Embedding in JPEG 111

8.2 Histogram Analysis 114

8.2.1 The JPEG Histogram 114

8.2.2 First-order Features 118

8.2.3 Second-order Features 119

8.2.4 Histogram Characteristic Function 121

8.3 Blockiness 122

8.4 Markov Model-based Features 124

8.5 Conditional Probabilities 126

8.6 Experiment and Comparison 128

9 Calibration Techniques 131

9.1 Calibrated Features 131

9.2 JPEG Calibration 133

9.2.1 The FRI-23 Feature Set 133

9.2.2 The Pevný Features and Cartesian Calibration 135

9.3 Calibration by Downsampling 137

9.3.1 Downsampling as Calibration 137

9.3.2 Calibrated HCF-COM 138

9.3.3 The Sum and Difference Images 139

9.3.4 Features for Colour Images 143

9.3.5 Pixel Selection 143

9.3.6 Other Features Based on Downsampling 145

9.3.7 Evaluation and Notes 146

9.4 Calibration in General 146

9.5 Progressive Randomisation 148

Part III Classifiers

10 Simulation and Evaluation 153

10.1 Estimation and Simulation 153

10.1.1 The Binomial Distribution 153

10.1.2 Probabilities and Sampling 155

10.1.3 Monte Carlo Simulations 156

10.1.4 Confidence Intervals 157

10.2 Scalar Measures 158

10.2.1 Two Error Types 158

10.2.2 Common Scalar Measures 160

10.3 The Receiver Operating Curve 161

10.3.1 The libSVM API for Python 161

10.3.2 The ROC Curve 164

10.3.3 Choosing a Point on the ROC Curve 167

10.3.4 Confidence and Variance 168

10.3.5 The Area Under the Curve 169

10.4 Experimental Methodology 170

10.4.1 Feature Storage 171

10.4.2 Parallel Computation 171

10.4.3 The Dangers of Large-scale Experiments 173

10.5 Comparison and Hypothesis Testing 173

10.5.1 The Hypothesis Test 174

10.5.2 Comparing Two Binomial Proportions 174

10.6 Summary 176

11 Support Vector Machines 179

11.1 Linear Classifiers 179

11.1.1 Linearly Separable Problems 180

11.1.2 Non-separable Problems 183

11.2 The Kernel Function 186

11.2.1 Example: The XOR Function 187

11.2.2 The SVM Algorithm 187

11.3 ν-SVM 189

11.4 Multi-class Methods 191

11.5 One-class Methods 192

11.5.1 The One-class SVM Solution 193

11.5.2 Practical Problems 194

11.5.3 Multiple Hyperspheres 195

11.6 Summary 196

12 Other Classification Algorithms 197

12.1 Bayesian Classifiers 198

12.1.1 Classification Regions and Errors 199

12.1.2 Misclassification Risk 200

12.1.3 The Naïve Bayes Classifier 201

12.1.4 A Security Criterion 202

12.2 Estimating Probability Distributions 203

12.2.1 The Histogram 204

12.2.2 The Kernel Density Estimator 204

12.3 Multivariate Regression Analysis 209

12.3.1 Linear Regression 209

12.3.2 Support Vector Regression 211

12.4 Unsupervised Learning 212

12.4.1 K-means Clustering 213

12.5 Summary 215

13 Feature Selection and Evaluation 217

13.1 Overfitting and Underfitting 217

13.1.1 Feature Selection and Feature Extraction 219

13.2 Scalar Feature Selection 220

13.2.1 Analysis of Variance 220

13.3 Feature Subset Selection 222

13.3.1 Subset Evaluation 223

13.3.2 Search Algorithms 224

13.4 Selection Using Information Theory 225

13.4.1 Entropy 225

13.4.2 Mutual Information 227

13.4.3 Multivariate Information 229

13.4.4 Information Theory with Continuous Sets 232

13.4.5 Estimation of Entropy and Information 233

13.4.6 Ranking Features 234

13.5 Boosting Feature Selection 238

13.6 Applications in Steganalysis 239

13.6.1 Correlation Coefficient 240

13.6.2 Optimised Feature Vectors for JPEG 241

14 The Steganalysis Problem 245

14.1 Different Use Cases 245

14.1.1 Who are Alice and Bob? 245

14.1.2 Wendy’s Role 247

14.1.3 Pooled Steganalysis 248

14.1.4 Quantitative Steganalysis 249

14.2 Images and Training Sets 250

14.2.1 Choosing the Cover Source 250

14.2.2 The Training Scenario 253

14.2.3 The Steganalytic Game 257

14.3 Composite Classifier Systems 258

14.3.1 Fusion 258

14.3.2 A Multi-layer Classifier for JPEG 260

14.3.3 Benefits of Composite Classifiers 261

14.4 Summary 262

15 Future of the Field 263

15.1 Image Forensics 263

15.2 Conclusions and Notes 265

Bibliography 267

Index 279