Representing Shapes

for Visual Recognition

Title 0

Abstract 1

Biography 2

Acknowledgements 3

Contents 4

Chapter 1. Introduction 6

• 1.1 Three observations 6
• 1.2 The problem 7
• 1.3 Recognition 7
• 1.4 Representations 10
• 1.5 Representations for recognition 13
• 1.6 Previous 2-D representations 15
• 1.7 Generalized cylinders 18
• 1.8 Philosophy of the approach 22

Chapter 2. Representing plane curves 25

• 2.1 Overview 25
• 2.2 Notation and terminology 25
• 2.3 Goals 26
• 2.4 Decoupling rotation and position 27
• 2.5 Scale independent parts 27
• 2.6 Contour codons 29
• 2.7 A perceptual note 34
• 2.8 Positive minima 35
• 2.9 Quantitative description of parts 36
• 2.10 Curves with cusps 37
• 2.11 Codon description extended for cusps 39
• 2.12 Codon hierarchies 42
• 2.13 Summary 43

Chapter 3. Representing surfaces 45

• 3.1 Surfaces of revolution 45
• 3.2 Notation and terminology 46
• 3.3 Goals 47
• 3.4 Decoupling rotation and position 47
• 3.5 Scale independent parts 48
• 3.6 Segmentation of developable surfaces 49
• 3.7 Segmentation of surfaces of revolution 52
• 3.8 Segmentation of the torus 56
• 3.9 Segmentation of the general ellipsoid 58
• 3.10 Flattened surfaces of revolution 63
• 3.11 Surfaces with discontinuities 67
• 3.12 Elbows 68
• 3.13 Summary 71

Chapter 4. Discovering natural scales 72

• 4.1 Differential quantities on fractal curves 73
• 4.2 Natural scale 74
• 4.3 Natural scale and effective dimension 87
• 4.4 Summary 90

Chapter 5. Relation to human perception 91

• 5.1 Predictions 91
• 5.2 Experiments 92
• 5.2 Demonstrations 97
• 5.4 Summary 106

Epilogue 108

References 111

Appendix 1. Lisp code 114

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