Interpretation of Visual Motion

Opis

Interpretation of Visual Motion: A Computational Study provides an information processing point of view to the phenomenon of visual motion.

This book discusses the computational theory formulated for recovering the scene from monocular visual motion, determining the local geometry and rigid body motion of surfaces from spatio-temporal parameters of visual motion. This compilation also provides a theoretical and computational framework for future research on visual motion, both in human vision and machine vision areas. Other topics include the computation of image flow from intensity derivatives, instantaneous image flow due to rigid motion, time and space-time derivatives of image flow, and estimation of maximum absolute error.

This publication is recommended for professionals and non-specialists intending to acquire knowledge of visual motion.

Spis treści

Front Cover 2
Dedication 4
Interpretation of Visual Motion: A Computational Study 5
Copyright Page 6
Table of Contents 7
Chapter 1. Introduction 15
- 1.1 Problem description 15
- 1.2 Motivations for the study 16
- 1.3 The approach 17
- 1.5 Summary of results 19
- 1.4 Strategy of formulation and analysis 19
- 1.6 Conclusions and new questions 21
- 1.7 Organization of the book 21
Chapter 2. Background 23
- 2.2 Visual ambiguity and assumptions 23

Front Cover 2
Dedication 4
Interpretation of Visual Motion: A Computational Study 5
Copyright Page 6
Table of Contents 7
Chapter 1. Introduction 15
- 1.1 Problem description 15
- 1.2 Motivations for the study 16
- 1.3 The approach 17
- 1.5 Summary of results 19
- 1.4 Strategy of formulation and analysis 19
- 1.6 Conclusions and new questions 21
- 1.7 Organization of the book 21
Chapter 2. Background 23
- 2.2 Visual ambiguity and assumptions 23
- 2.1 Introduction 23
- 2.3 Discrete approach 25
- 2.4 Continuous approach 27
- 2.5 Interpretation of image flow 33
- 2.6 Some comments on the approaches 34
- 2.7 What is new? 34
Chapter 3. Formulation 35
- 3.1 Computational theory and approach 35
- 3.2 Image formation 36
- 3.3 Formulation: instantaneous image flow due to rigid motion 39
- 3.4 The nature of the image flow equations 44
Chapter 4. Solving the Image Flow Equations 46
- 4.1 Solution for motion and slopes in terms of θ and r 46
- 4.2 Planar surfaces 48
- 4.3 Curved surfaces 59
- 4.4 Overall summary of the nature of the solutions 65
- 4.5 Fully reduced flow parameters for image flow analysis 66
Chapter 5. Using Temporal Information: Rigid Motion 71
- 5.1 Formulation and solution 72
- 5.2 Relating the first order image flow parameters and scene parameters 73
- 5.3 Rigid and uniform motion 74
- 5.4 The case when the direction of V changes 76
- 5.5 Accelerated motions 79
Chapter 6. The General Formulation 81
- 6.1 Representation and formulation 81
- 6.2 Arbitrarily time-varying 3D scenes: non-rigid and non-uniform motion of general surfaces 85
Chapter 7. Error Sensitivity and Numerical Examples 89
- 7.1 Estimation of maximum absolute error 89
- 7.2 Numerical examples of multiple solution cases 91
Chapter 8. Conclusions 97
APPENDICES 99
- Appendices A: Expressing a surface in terms of image coordinates 99
- Appendices B: Some degenerate cases and conditions 101
  - 1 Some degenerate cases 101
  - 3 Condition for the moving surface to be curved 103
  - 2 Condition for the moving surface to be planar 103
  - 4 Solution for orientation and motion in terms of r and θ 104
- Appendices C: Solving the image flow equations: planar surfaces 105
  - 1 Bounds from first order flow parameters 109
  - 2 A method for determining the structure and motion parameters 110
  - 3 Solving for θ and r 111
  - 4 Summary of the solution method 112
  - 5 Interpretation of the bounds on Vz and Ωz 112
- Appendices D: Nature of solutions for planar surfaces 116
  - 1 Relation between the two interpretations 118
- Appendices E: Resolving the ambiguity of interpretation: planar surfaces 119
  - 1 Evolution of planar surface solutions 121
  - 2 Uniqueness of interpretation: two flow fields 123
- Appendices F: Solving the image flow equations: curved surfaces 126
  - 1 Solution for curvatures 126
  - 2 Constraints on r and θ 127
  - 3 Summary of computational algorithm 128
- Appendices G: Conditions for multiple interpretations: curved surfaces 129
  - 1 Solutions for θ 129
  - 2 Multiple interpretations due to multiple solutions for θ 130
  - 3 Multiple interpretations due to multiple solutions for r 136
  - 4 Condition for uniqueness of interpretation 138
- Appendices H: Solving for θ when the direction of V changes 139
- Appendices I: Solving for r and θ when the camera tracks a point 141
- Appendices J: Surface deformation parameters 142
  - 1 Interpretation of the velocity gradient tensor 142
  - 2 Interpretation of the motion and deformation parameters aij 143
- Bibliography 144
- Index 152

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