### Correction of geometric perceptual distortions in pictures

#### M.S. Thesis by Denis Zorin, Caltech, 1995

Complete thesis, Compressed PostScript  (9.8 MB)

Each chapter below has a link to a compressed PostScript file.

1 Introduction 1 (1.1 MB)

1.1 Motivation 1
1.2 Contributions 2
1.3 Perspective Projection and Viewing Position Nomenclature3
1.4 Summary 6

2 Perception of Pictures 8 (3.7 MB)

2.1 Assumptions and Definitions 9
2.1.1 Perceptual Nomenclature 9
2.1.2 Defining Pictures 12
2.2 Robustness of Pictures 16
2.3 Perception of Objects in Pictures. 19
2.3.1 Rectangular Objects 19
2.3.2 Spheres, Cylinders, Humans and Animals 21
2.3.3 Foreshortening 22
2.4 Other Properties of Visual Perception 24
2.4.1 Visual Field 24
2.4.2 Perception of Straightness and Curvature 24
2.4.3 Perception of Verticality 25
2.5 Linear Perspective 25
2.5.1 Rectangular Objects in Linear Perspective 27
2.5.2 Spheres, Cylinders, Humans 29
2.5.3 Straightness, Verticality, Texture Density, Movement 30
2.6 Other Traditional Perspective Systems 32
2.7 Summary 37

3 Formalization of Perceptual Requirements 40 (100 KB)

3.1 Technical Requirements 40
3.2 Structural Requirements 41
3.2.1 Definitions and Preliminary Lemmas 42
3.2.2 Holes in Images 46
3.2.3 Loops, Folds and Twists 50
3.2.4 Loops and Twists 53
3.2.5 Decomposition 59
3.3 Nonstructural Requirements 60
3.3.1 Definitions 60
3.3.2 Zero Curvature Condition 61
3.3.3 Direct View Condition 64
3.3.4 Error Functionals 67
3.3.5 Optimization Problem 68

4 Construction of Projections 71 (389 KB)

4.1 Previous Work 71
4.2 Perceptually-based systems 71
Reggini's perspective 71
Raushenbakh's system 72
4.2.1 Artistic systems 73
4.2.2 Technical Projections 75
4.3 Axially Symmetric Projection 76
4.3.1 Reformulation of the Problem 76
4.3.2 Limiting Cases 78
4.3.3 Lower Bound of the Optimal Values of F 79
4.3.4 Second Bound 82
4.3.5 Interpolations 85
4.3.6 Extentions 87

5 Implementation and Applications 8 (1.9 MB)

5.1 Implementation. 88
5.2 Deep and Shallow Scenes: When Do We Need a Wide-Angle Projection? 90
5.3 Applications of Correcting Transformations 93
5.4 Other Applications 96
Zooming. 96
Extremely wide angle images. 98
5.5 Summary 98

6 Conclusions and Future Work 100 (12 KB)

6.1 Conclusions 100
6.2 Future Work 101

Appendices:

A.1 Robustness and Perception of the Picture Surface and Frame 103
A.2 Rigidity in Motion Pictures 108
A.3 Size and Distance in Pictures 110
A.4 Orientation and Layout 113
A.5 Rectangular Corners 122
A.6 Foreshortening 126
A.7 Visual field 131
A.8 Straightness and Curvature 133
A.9 Verticality 137

Bibliography 146 (21 KB)