Shared Gaussian Process Latent Variables Models - Oxford Brookes ...

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CONTENTS 5 4.4.1 Extracting the first orthogonal direction . . . . . . . . . . 85 4.4.2 Extracting consecutive directions . . . . . . . . . . . . . 86 4.4.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.5 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5 Applications 92 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2 Human Pose Estimation . . . . . . . . . . . . . . . . . . . . . . . 92 5.2.1 Generative . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.2.2 Discriminative . . . . . . . . . . . . . . . . . . . . . . . 94 5.2.3 Problem Statement . . . . . . . . . . . . . . . . . . . . . 94 5.3 Image Features . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.3.1 Shapeme Features . . . . . . . . . . . . . . . . . . . . . 95 5.3.2 Histogram of Oriented Gradients . . . . . . . . . . . . . . 97 5.4 Data-sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.5 <strong>Shared</strong> back-constrained GP-LVM . . . . . . . . . . . . . . . . . 100 5.5.1 Single Image Inference . . . . . . . . . . . . . . . . . . . 102 5.5.2 Sequential Inference . . . . . . . . . . . . . . . . . . . . 103 5.6 Subspace GP-LVM . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.6.1 Single Image Inference . . . . . . . . . . . . . . . . . . . 107 5.6.2 Sequential Inference . . . . . . . . . . . . . . . . . . . . 108 5.7 Quantitative Results . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.8 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.9 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6 CONTENTS 5.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6 Conclusions 119 6.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.2 Review of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 119 6.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Page 1 and 2: Shared Gaussian Process Latent Vari
Page 3 and 4: Acknowledgements 2
Page 5: 4 CONTENTS 2.7.2 Training . . . . .
Page 9 and 10: 8 LIST OF FIGURES 3.11 Toy data3: l
Page 11 and 12: Chapter 1 Introduction Information
Page 13 and 14: 12 CHAPTER 1. INTRODUCTION current
Page 15 and 16: Chapter 2 Background 2.1 Introducti
Page 17 and 18: 16 CHAPTER 2. BACKGROUND 1 0.9 0.8
Page 19 and 20: 18 CHAPTER 2. BACKGROUND X to its o
Page 21 and 22: 20 CHAPTER 2. BACKGROUND dimensions
Page 23 and 24: 22 CHAPTER 2. BACKGROUND approximat
Page 25 and 26: 24 CHAPTER 2. BACKGROUND diagonal c
Page 27 and 28: 26 CHAPTER 2. BACKGROUND unraveled.
Page 29 and 30: 28 CHAPTER 2. BACKGROUND apply an a
Page 31 and 32: 30 CHAPTER 2. BACKGROUND be connect
Page 33 and 34: 32 CHAPTER 2. BACKGROUND Local Line
Page 35 and 36: 34 CHAPTER 2. BACKGROUND 15 10 5 0
Page 37 and 38: 36 CHAPTER 2. BACKGROUND by W, Figu
Page 39 and 40: 38 CHAPTER 2. BACKGROUND Figure 2.4
Page 41 and 42: 40 CHAPTER 2. BACKGROUND X ∈ ℜ
Page 43 and 44: 42 CHAPTER 2. BACKGROUND 2.5 2 1.5
Page 45 and 46: 44 CHAPTER 2. BACKGROUND rupted by
Page 47 and 48: 46 CHAPTER 2. BACKGROUND where ˜ C
Page 49 and 50: 48 CHAPTER 2. BACKGROUND prior over
Page 51 and 52: 50 CHAPTER 2. BACKGROUND generative
Page 53 and 54: 52 CHAPTER 2. BACKGROUND the latent
Page 55 and 56: 54 CHAPTER 2. BACKGROUND 2.9 Shared
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56 CHAPTER 2. BACKGROUND Y X Figure
Page 59 and 60:
58 CHAPTER 2. BACKGROUND Gaussian p
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60 CHAPTER 3. SHARED GP-LVM sponden
Page 63 and 64:
62 CHAPTER 3. SHARED GP-LVM makes m
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64 CHAPTER 3. SHARED GP-LVM where t
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66 CHAPTER 3. SHARED GP-LVM 4 3 2 1
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68 CHAPTER 3. SHARED GP-LVM 1 0.8 0
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70 CHAPTER 3. SHARED GP-LVM Example
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72 CHAPTER 3. SHARED GP-LVM 0.3 0.2
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74 CHAPTER 3. SHARED GP-LVM φ Y X
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76 CHAPTER 3. SHARED GP-LVM leading
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78 CHAPTER 3. SHARED GP-LVM servati
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Chapter 4 NCCA 4.1 Introduction In
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82 CHAPTER 4. NCCA as u Y i = x S
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84 CHAPTER 4. NCCA X Y Z X X S Y Z
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86 CHAPTER 4. NCCA By pre-multiplyi
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88 CHAPTER 4. NCCA 1 0.8 0.6 0.4 0.
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90 CHAPTER 4. NCCA 4.5 Extensions W
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Chapter 5 Applications 5.1 Introduc
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94 CHAPTER 5. APPLICATIONS as optic
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96 CHAPTER 5. APPLICATIONS of an im
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98 CHAPTER 5. APPLICATIONS histogra
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100 CHAPTER 5. APPLICATIONS the dat
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102 CHAPTER 5. APPLICATIONS Figure
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104 CHAPTER 5. APPLICATIONS the GP
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106 CHAPTER 5. APPLICATIONS varianc
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108 CHAPTER 5. APPLICATIONS locatio
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Page 113 and 114:
112 CHAPTER 5. APPLICATIONS Error (
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Page 117 and 118:
116 CHAPTER 5. APPLICATIONS over th
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118 CHAPTER 5. APPLICATIONS age rep
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120 CHAPTER 6. CONCLUSIONS vated an
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122 CHAPTER 6. CONCLUSIONS a shared
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124 BIBLIOGRAPHY [7] S. Belongie, J
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126 BIBLIOGRAPHY [24] K. Grochow, S
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128 BIBLIOGRAPHY [39] D. MacKay. Ba
Page 131 and 132:
130 BIBLIOGRAPHY [56] H. A. Simon.
Page 133 and 134:
132 BIBLIOGRAPHY [74] S. Wachter an
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