Motion Understanding

1 Bounding Constraint Propagation for Optical Flow Estimation.- 1.1 Introduction.- 1.2 The Gradient Constraint Equation.- 1.3 Gradient-Based Algorithms.- 1.4 Coping with Smoothness Violations.- 1.4.1 Thresholding for Smoothness.- 1.4.2 Continuous Adaptation to Errors.- 1.5 Results.- 1.6 Discussion.- 2 Image Flow: Fundamentals and Algorithms.- 2.1 Introduction.- 2.1.1 Background.- 2.1.2 Applications for Image Flow.- 2.1.3 Summary.- 2.2 Simple Image Flows.- 2.2.1 Image Flow Equation for Simple Flows.- 2.2.2 Algorithms for Simple Image Flows.- 2.2.3 Summary of Simple Image Flows.- 2.3 Discontinuous Image Flow.- 2.3.1 Surfaces and Projections.- 2.3.2 Image Irradiance Discontinuities.- 2.3.3 Velocity Field Discontinuities.- 2.3.4 Validity of the Image Flow Equation.- 2.3.5 Related Work.- 2.4 Analysis of Discontinuous Image Flows.- 2.4.1 Discontinuities in Continuous Image Functions.- 2.4.2 Sampling of Discontinuous Image Flows.- 2.4.3 Directional Selectivity.- 2.4.4 Summary of Discontinuous Image Flows.- 2.5 Algorithms for Discontinuous Image Flows.- 2.5.1 Background.- 2.5.2 Problem Statement.- 2.5.3 Constraint Line Clustering.- 2.5.4 Summary.- 2.6 Smoothing Discontinuous Image Flows.- 2.6.1 Motion Boundary Detection.- 2.6.2 Velocity Field Smoothing.- 2.6.3 Interleaved Detection and Smoothing.- 2.7 Summary and Conclusions.- 3 A Computational Approach to the Fusion of Stereopsis and Kineopsis.- 3.1 Introduction.- 3.2 Integrating Optical Flow to Stereopsis for Motion.- 3.3 Perception of Rigid Objects in Motion.- 3.4 Examples.- 3.5 Summary.- 4 The Empirical Study of Structure from Motion.- 4.1 Introduction.- 4.2 Viewer-Centered vs. Object-Centered Depth.- 4.2.1 Orthographic Projections of Rotation in Depth.- 4.2.2 Recovery of Structure from Velocity Gradients.- 4.3 The Correspondence Problem.- 4.3.1 Point Configurations.- 4.3.2 Contour Deformation.- 4.3.3 Texture Deformation.- 4.4 Rigidity.- 4.5 Perception of Self Motion.- 4.6 A Theory of Observers.- 4.7 An Empirical Test of Constraints.- 4.8 Summary and Conclusions.- 5 Motion Estimation Using More Than Two Images.- 5.1 Introduction.- 5.2 General Description of the Method.- 5.2.1 Establishing the Equations.- 5.2.2 Simplifying the Equations.- 5.2.3 Solving the Equations.- 5.2.4 Calculating the Motion Parameters.- 5.2.5 Advantages of this Approach.- 5.2.6 Limitations of Our Approach.- 5.3 Results.- 5.3.1 Synthetic Test Data.- 5.3.2 Real Test Data.- 5.4 Comparison with Other Methods.- 5.4.1 Error Analysis.- 5.5 Conclusions.- 6 An Experimental Investigation of Estimation Approaches for Optical Flow Fields.- 6.1 Introduction.- 6.2 Feature Based Estimation.- 6.2.1 The Monotonicity Operator.- 6.2.2 From Feature Positions to Optical Flow Vectors.- 6.2.3 Test Sequence.- 6.2.4 Moving Object Detection.- 6.2.5 Performance Analysis of the Monotonicity Operator.- 6.2.6 Robustness of the Monotonicity Operator Against Parameter Changes.- 6.2.7 Reduction to Two Classes.- 6.3 Analytical Approach for the Estimation of Optical Flow Vector Fields.- 6.3.1 The “Oriented Smoothness” Constraint.- 6.3.2 Evaluation at Local Extrema of the Picture Function.- 6.4 Discussion.- 7 The Incremental Rigidity Scheme and Long-Range Motion Correspondence.- 7.1 The Rigidity-Based Recovery of Structure from Motion.- 7.1.1 The Perception of Structure from Motion by Human Observers.- 7.1.2 Computational Studies of the Recovery of Structure from Motion.- 7.1.3 Additional Requirements for the Recovery of Structure from Motion.- 7.1.4 A Hypothesis: Maximizing Rigidity Relative to the Current Internal Model.- 7.2 The Incremental Rigidity Scheme.- 7.2.1 The Basic Scheme.- 7.2.2 Possible Modifications.- 7.2.3 Implementation.- 7.3 Experimental Results.- 7.3.1 Rigid Motion.- 7.3.2 Non-Rigid Motion.- 7.4 Additional Properties of the Incremental Rigidity Scheme.- 7.4.1 Orthographic and Perspective Projections.- 7.4.2 The Effect of the Number of Points.- 7.4.3 On Multiple Objects.- 7.4.4 Convergence to the Local Minimum.- 7.5 Possible Implications to the Long-Range Motion Correspondence Process.- 7.6 Summary.- 8 Some Problems with Correspondence.- 8.1 Introduction.- 8.2 Determining Correspondence.- 8.3 Correspondence in Computer Vision.- 8.3.1 Correspondence in Stereopsis Algorithms.- 8.3.2 Correspondence in Temporal Matching Algorithms.- 8.4 An Experiment on Correspondence.- 8.5 Conclusions.- 9 Recovering Connectivity from Moving Point-Light Displays.- 9.1 Introduction.- 9.2 Motion Information is a Minimal Stimulus Condition for the Perception of Form.- 9.3 Processing Models for Recovering Form from Motion.- 9.4 Do Fixed-Axis Models Predict Human Performance?.- 9.5 Human Implementation of Additional Processing Constraints.- 9.5.1 Centers of Moment.- 9.5.2 Occlusion’s Effect on Depth Order and Implicit Form.- 9.5.3 Common Motion as Grouping Factor.- 9.5.4 Proximity.- 9.5.5 Familiarity.- 9.6 Incompatibilities Between Human Performance and Models Seeking Local Rigidity.- 9.6.1 Human Capabilities That Exceed Fixed-Axis Models: The Local Rigidity Assumption.- 9.6.2 Human Performance Limitations.- 9.7 Conclusion.- 10 Algorithms for Motion Estimation Based on Three-Dimensional Correspondences.- 10.1 Introduction.- 10.2 Direct Linear Method.- 10.3 Method Based on Translation Invariants.- 10.4 Axis-Angle Method.- 10.5 The Screw Decomposition Method.- 10.6 Improved Motion Estimation Algorithms.- 10.7 Comparing the Linear and Nonlinear Methods.- 10.8 Simulation Results for Three-Point Methods.- 10.9 Some Recent Related Results.- 11 Towards a Theory of Motion Understanding in Man and Machine.- 11.1 Introduction.- 11.2 The Time Complexity of Visual Perception.- 11.2.1 The Role of Time in Vision.- 11.2.2 The Nature of the Computational Problem.- 11.2.3 Implications.- 11.3 Measurement and Hierarchical Representations in Early Vision.- 11.3.1 What is Measurement?.- 11.3.2 Directional Information and its Measurement.- 11.3.3 Hierarchical Processing.- 11.3.4 Construction of Orientation or Velocity Selective Filters.- 11.4 Biological Research.- 11.5 Machine Research.- Author Index.