Motion Understanding: Robot and Human Vision

W. Bach, J.K. Aggarwal

Springer Science & Business Media, Feb 29, 1988 - Technology & Engineering - 432 pages

The physical processes which initiate and maintain motion have been a major concern of serious investigation throughout the evolution of scientific thought. As early as the fifth century B. C. questions regarding motion were presented as touchstones for the most fundamental concepts about existence. Such wide ranging philosophical issues are beyond the scope of this book, however, consider the paradox of the flying arrow attri buted to Zeno of Elea: An arrow is shot from point A to point B requiring a sequence of time instants to traverse the distance. Now, for any time instant, T, of the sequence the arrow is at a position, Pi' and at Ti+! the i arrow is at Pi+i> with Pi ::I-P+• Clearly, each Ti must be a singular time i 1 unit at which the arrow is at rest at Pi because if the arrow were moving during Ti there would be a further sequence, Til' of time instants required for the arrow to traverse the smaller distance. Now, regardless of the level to which this recursive argument is applied, one is left with the flight of the arrow comprising a sequence of positions at which the arrow is at rest. The original intent of presenting this paradox has been interpreted to be as an argument against the possibility of individuated objects moving in space.

Contents

• Bounding Constraint Propagation for Optical Flow Estimation: 1
• 12 The Gradient Constraint Equation: 2
• 13 GradientBased Algorithms: 3
• 14 Coping with Smoothness Violations: 5
• 142 Continuous Adaptation to Errors: 7
• 15 Results: 12
• 16 Discussion: 17
• Image Flow Fundamentals and Algorithms: 23
• 211 Background: 24
• 272 Applications for Image Flow: 26
• 213 Summary: 30
• 221 Image Flow Equation for Simple Flows: 31
• 222 Algorithms for Simple Image Flows: 32
• 223 Summary of Simple Image Flows: 36
• 23 Discontinuous Image Flow: 37
• 232 Image Irradiance Discontinuities: 39
• 233 Velocity Field Discontinuities: 41
• 234 Validity of the Image Flow Equation: 42
• 24 Analysis of Discontinuous Image Flows: 44
• 242 Sampling of Discontinuous Image Flows: 48
• 243 Directional Selectivity: 51
• 244 Summary of Discontinuous Image Flows: 53
• 25 Algorithms for Discontinuous Image Flows: 54
• 252 Problem Statement: 55
• 253 Constraint Line Clustering: 56
• 254 Summary: 60
• 26 Smoothing Discontinuous Image Flows: 62
• 261 Motion Boundary Detection: 63
• 262 Velocity Field Smoothing: 64
• 265 Interleaved Detection and Smoothing: 67
• 27 Summary and Conclusions: 68
• A Computational Approach to the Fusion of Stereopsis and Kineopsis: 81
• 32 Integrating Optical Flow to Stereopsis for Motion: 83
• 33 Perception of Rigid Objects in Motion: 88
• 34 Examples: 91
• 35 Summary: 95
• The Empirical Study of Structure from Motion: 101
• 42 ViewerCentered vs ObjectCentered Depth: 102
• 421 Orthographic Projections of Rotation in Depth: 106
• 422 Recovery of Structure from Velocity Gradients: 110
• 43 The Correspondence Problem: 113
• 431 Point Configurations: 114
• 432 Contour Deformation: 116
• 433 Texture Deformation: 119
• 44 Rigidity: 120
• 45 Perception of Self Motion: 125
• 46 A Theory of Observers: 127
• 47 An Empirical Test of Constraints: 132
• 48 Summary and Conclusions: 135
• Motion Estimation Using More Than Two Images: 143
• 52 General Description of the Method: 146
• 521 Establishing the Equations: 150
• 522 Simplifying the Equations: 154
• 523 Solving the Equations: 156
• 524 Calculating the Motion Parameters: 157
• 525 Advantages of this Approach: 159
• 526 Limitations of Our Approach: 162
• 53 Results: 163
• 531 Synthetic Test Data: 164
• 532 Real Test Data: 170
• 54 Comparison with Other Methods: 182
• 541 Error Analysis: 183
• 55 Conclusions: 184
• An Experimental Investigation of Estimation Approaches for Optical Flow Fields: 189
• 62 Feature Based Estimation: 191
• 622 From Feature Positions to Optical FlowVectors: 195
• 624 Moving Object Detection: 197
• 625 Performance Analysis of the Monotonicity Operator: 199
• 626 Robustness of the Monotonicity Operator Against Parameter Changes: 206
• 627 Reduction to Two Classes: 208
• 63 Analytical Approach for the Estimation of Optical Flow Vector Fields: 210
• 631 The Oriented Smoothness Constraint: 211
• 632 Evaluation at Local Extrema of the Picture Function: 216
• 64 Discussion: 217
• The Incremental Rigidity Scheme and LongRange Motion Correspondence: 227
• 712 Computational Studies of the Recovery of Structure from Motion: 228
• 713 Additional Requirements for the Recovery of Structure from Motion: 230
• Maximizing Rigidity Relative to the Current Internal Model: 232
• 72 The Incremental Rigidity Scheme: 234
• 721 The Basic Scheme: 235
• 722 Possible Modifications: 238
• 723 Implementation: 239
• 731 Rigid Motion: 242
• 732 NonRigid Motion: 249
• 74 Additional Properties of the Incremental Rigidity Scheme: 251
• 742 The Effect of the Number of Points: 252
• 743 On Multiple Objects: 256
• 744 Convergence to the Local Minimum: 257
• 75 Possible Implications to the LongRange Motion Correspondence Process: 258
• 76 Summary: 260
• Some Problems with Correspondence: 269
• 82 Determining Correspondence: 275
• 83 Correspondence in Computer Vision: 276
• 832 Correspondence in Temporal Matching Algorithms: 278
• 84 An Experiment on Correspondence: 282
• 85 Conclusions: 289
• Recovering Connectivity from Moving PointLight Displays: 297
• 92 Motion Information is a Minimal Stimulus Condition for the Perception of Form: 299
• 93 Processing Models for Recovering Form from Motion: 301
• 94 Do FixedAxis Models Predict Human Performance?: 304
• 95 Human Implementation of Additional Processing Constraints: 307
• 952 Occlusions Effect on Depth Order and Implicit Form: 309
• 953 Common Motion as a Grouping Factor: 314
• 954 Proximity: 315
• 955 Familiarity: 316
• 96 Incompatibilities Between Human Performance and Models Seeking Local Rigidity: 319
• 962 Human Performance Limitations: 320
• 97 Conclusion: 321
• Algorithms for Motion Estimation Based on ThreeDimensional Correspondences: 329
• 102 Direct Linear Method: 332
• 103 Method Based on Translation Invariants: 333
• 104 AxisAngle Method: 336
• 105 The Screw Decomposition Method: 338
• 106 Improved Motion Estimation Algorithms: 343
• 107 Comparing the Linear and Nonlinear Methods: 344
• 108 Simulation Results for ThreePoint Methods: 346
• 109 Some Recent Related Results: 348
• Towards a Theory of Motion Understanding in Man and Machine: 353
• 112 The Time Complexity of Visual Perception: 355
• 1122 The Nature of the Computational Problem: 360
• 1123 Implications: 366
• 113 Measurement and Hierarchical Representations in Early Vision: 369
• 1132 Directional Information and its Measurement: 370
• 1133 Hierarchical Processing: 377
• 1134 Construction of Orientation or Velocity Selective Filters: 379
• 114 Biological Research: 404
• 115 Machine Research: 408
• Author Index: 419
• Subject Index: 425

Bibliographic information

• Title: Motion Understanding: Robot and Human Vision; Volume 44 of The Springer International Series in Engineering and Computer Science
• Editors: W. Bach, J.K. Aggarwal
• Edition: illustrated
• Publisher: Springer Science & Business Media, 1988
• ISBN: 0898382580, 9780898382587
• Length: 432 pages
• Subjects: Technology & Engineering / Automation; Technology & Engineering / Electrical