List of Figures............................................................................................................................................ VI
List of Tables........................................................................................................................................... XIII
Acknowledgements.............................................................................................................................. XV
Abstract....................................................................................................................................................... XVI
CHAPTER 1 Introduction..................................................................................................................... 1
1.1. Motivation and Background...................................................................... 1
1.2. Scope of Research...................................................................................... 3
1.3. Original Work............................................................................................... 4
1.4. Organisation of This Thesis....................................................................... 6
CHAPTER 2
Rotation Invariant Texture Classification................................. 8
2.1. What is Texture?........................................................................................... 8
2.1.1. Some Definitions of
Texture........................................................................... 9
2.1.2. Texture in Visual
Perception........................................................................ 10
2.1.3. 3D Surface Relief and
Albedo...................................................................... 10
2.2. Texture Features....................................................................................... 12
2.2.1. Three Stages of
Texture Classification System.............................................. 13
2.2.2. Surveys...................................................................................................... 14
2.2.3. Texture Feature
Methods............................................................................. 14
2.3. Image Rotation Invariant Features........................................................ 21
2.3.1. Introduction................................................................................................ 21
2.3.2. Statistical Methods..................................................................................... 22
2.3.3. Model Based Methods................................................................................. 23
2.4. Surface Rotation Invariant Features................................................... 26
2.5. Summary....................................................................................................... 28
CHAPTER 3 From Surface to Image............................................................................................ 30
3.1. Introduction................................................................................................ 30
3.1.1. Surface Roughness..................................................................................... 30
3.1.2. Illumination Geometry.................................................................................. 33
3.1.3. Diffuse and Specular................................................................................... 34
3.2. Reflection and Illumination modelling.................................................. 35
3.2.1. Review of Related Work.............................................................................. 35
3.2.2. Lambertian Illumination Model...................................................................... 39
3.3. Kube-Pentland Surface Model................................................................ 41
3.3.1. Theory....................................................................................................... 41
3.3.2. Frequency Domain Responses..................................................................... 43
3.3.3. Directional Filter.......................................................................................... 44
3.3.4. Non-linear Effects....................................................................................... 48
3.3.5. Effect of Shadowing.................................................................................... 53
3.3.6. Summary of Kube-Pentland Model................................................................ 56
3.4. Descriptions of Synthetic Surface....................................................... 57
3.5. Image-based Classification vs. Surface-based Classification........ 60
3.6. Summary....................................................................................................... 62
CHAPTER 4 Photometric
Stereo................................................................................................. 63
4.1. Candidate Surface Recovering Methods.............................................. 63
4.1.1. Motivation................................................................................................... 63
4.1.2. Binocular Stereo......................................................................................... 64
4.1.3. Shape from shading from a single image....................................................... 65
4.1.4. Photometric stereo...................................................................................... 67
4.2. A General Review of the Development of Photometric Stereo..... 69
4.3. Three Image Based Photometric Stereo............................................... 72
4.3.1. Three Photometric Images........................................................................... 72
4.3.2. Equations of Photometric Stereo.................................................................. 73
4.3.3. Separating Gradient and Albedo using Photometric
Stereo............................. 75
4.4. Improvement on Three Image Based Photometric Stereo................ 76
4.5. Summary....................................................................................................... 78
CHAPTER 5 Gradient Space............................................................................................................... 80
5.1. Introduction................................................................................................ 80
5.2. Extended Gaussian Image.......................................................................... 80
5.3. From Surface Normal to Gradient Space............................................ 82
5.4. Surface Orientation in Gradient Space................................................. 84
5.4.1. Surface Distribution of Gradient Space......................................................... 84
5.4.2. Presentation of Surface Orientation in Gradient Space................................... 86
5.4.3. Estimate Surface Orientation by Moment..................................................... 89
5.5. Summary....................................................................................................... 91
CHAPTER 6 An Algorithm of
Rotation Invariant Texture Classification 94
6.1. Introduction................................................................................................ 94
6.2. Surface Rotation-Invariant Texture Features.................................... 95
6.2.1 Related Work.............................................................................................. 96
6.2.2 Development of Features in Frequency Domain.............................................. 96
6.3. Photometric Stereo in Frequency Domain Dual................................ 101
6.3.1 Difficulties in Photometric Stereo................................................................. 101
6.3.2 Frequency Domain Dual.............................................................................. 102
6.3.3 Directional Characteristic of M(w, q)............................................................. 104
6.3.4 Summary................................................................................................... 109
6.4. Polar Spectrum........................................................................................ 110
6.4.1 Introduction............................................................................................... 110
6.4.2 Definition of Polar Spectrum........................................................................ 111
6.4.3 Drawbacks and Solutions........................................................................... 113
6.4.4 Polar Spectrum is a Function of Texture Directionality................................... 118
6.4.5 Polar Spectrum at Different Surface Orientations.......................................... 121
6.4.6 Estimation of Surface Orientation via Polar Spectrum.................................... 122
6.4.7 Summary................................................................................................... 127
6.5. Classifier................................................................................................... 128
6.6. Summary of the Complete Algorithm.................................................. 130
6.6.1 Surface Rotation Invariant Classification Scheme Using
Photometric Stereo (Surface Information) 130
6.6.2 Texture Classification Scheme Using Image Information
Only........................ 133
CHAPTER 7 Experiment and
Results...................................................................................... 135
7.1. Introduction and Aims of the Experiment............................................ 135
7.2. A Photometric Texture Database.......................................................... 136
7.2.1. Introduction.............................................................................................. 136
7.2.2. Comparison with Other Existing Texture Databases...................................... 137
7.2.3. Developing Our Photometric Texture Database............................................ 143
7.2.4. Set Up Photometric Texture Database........................................................ 144
7.2.5. Texture Samples....................................................................................... 145
7.3. Settings of the Experimental Apparatus........................................... 149
7.4. Experimental Procedure........................................................................ 152
7.4.1. Partitioning the Training and Test Textures.................................................. 152
7.4.2. Extracting Features................................................................................... 155
7.4.3. Classification............................................................................................ 155
7.5. Presentation of Experimental Results............................................... 156
7.5.1. Synthetic Textures.................................................................................... 156
7.5.2. Real Textures........................................................................................... 160
7.5.3. Comparative Study on Other State-of-the-art
Approaches.............................. 163
7.6. Summary..................................................................................................... 166
CHAPTER 8 A New
Classification Feature Space and A New Feature Generator 167
8.1. Introduction............................................................................................... 167
8.2. An Additional Feature Space: Radial Spectrum................................. 168
8.2.1. Misclassification and Motivation.................................................................. 168
8.2.2. Definition of Radial Spectrum..................................................................... 170
8.2.3. Examination of Radial Spectrum Insensitivity to
Surface Rotation.................. 173
8.2.4. Surface-based Classification Using Radial Spectra
Only............................... 174
8.2.5. Image-based Classification Using Radial Spectra Only................................. 177
8.3. New Feature Generator: Albedo Spectra.......................................... 179
8.3.1. Misclassification and Motivation.................................................................. 179
8.3.2. New Feature Generator: Albedo.................................................................. 181
8.3.3. Feature Characteristics on Albedo.............................................................. 185
8.3.4. Albedo Feature Sensitivity to Surface Rotation............................................ 187
8.3.5. Developing New Classifiers........................................................................ 188
8.3.6. Classification Results on Albedo Data Only................................................. 193
8.3.7. Comparative Study of Classification Results Between
Gradient Data and Albedo Data 195
8.4. An Improved Surface Rotation Invariant Classification Scheme
by Combining Feature Spaces and Feature Generators................................................................................ 198
8.4.1. Summary of Classification Scheme............................................................ 198
8.4.2. Classification Results................................................................................ 200
8.5. Summary..................................................................................................... 201
CHAPTER 9 Classification
Scheme Using Modified Photometric Stereo and 2D Spectra Comparison.......................................................................................................................................... 202
9.1. Introduction............................................................................................... 202
9.2. Photometric Stereo Using More Images............................................. 203
9.2.1. Introduction.............................................................................................. 203
9.2.2. The Problem of Shadows in PS3................................................................ 203
9.2.3. Existing Photometric Stereo Techniques (PS3) Obtained
from Different Light Sets 206
9.2.4. A New Strategy of Photometric Stereo by Using Four
Light Sources (PS4)..... 208
9.2.5. Improved Experimental Results.................................................................. 212
9.3. Classification Scheme Using 2D Spectra Comparison...................... 216
9.3.1. Classification Scheme............................................................................... 216
9.3.2. Classification Results................................................................................ 218
9.3.3. Comparing with Varma and Zisserman’s Method........................................... 220
9.4. Summary..................................................................................................... 221
CHAPTER 10 Summary and
Conclusion................................................................................ 222
10.1. Summary.................................................................................................... 222
10.2. Future Work............................................................................................ 225
10.3. Conclusion............................................................................................... 226
Reference..................................................................................................................................................... 228
