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.

Inhalt
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.- 1.5 Results.- 1.6 Discussion.- 2 Image Flow: Fundamentals and Algorithms.- 2.1 Introduction.- 2.2 Simple Image Flows.- 2.3 Discontinuous Image Flow.- 2.4 Analysis of Discontinuous Image Flows.- 2.5 Algorithms for Discontinuous Image Flows.- 2.6 Smoothing Discontinuous Image Flows.- 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.- 4.3 The Correspondence Problem.- 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.- 5.3 Results.- 5.4 Comparison with Other Methods.- 5.5 Conclusions.- 6 An Experimental Investigation of Estimation Approaches for Optical Flow Fields.- 6.1 Introduction.- 6.2 Feature Based Estimation.- 6.3 Analytical Approach for the Estimation of Optical Flow Vector Fields.- 6.4 Discussion.- 7 The Incremental Rigidity Scheme and Long-Range Motion Correspondence.- 7.1 The Rigidity-Based Recovery of Structure from Motion.- 7.2 The Incremental Rigidity Scheme.- 7.3 Experimental Results.- 7.4 Additional Properties of the Incremental Rigidity Scheme.- 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.- 8.4 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.- 9.6 Incompatibilities Between Human Performance and Models Seeking Local Rigidity.- 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.- 11.3 Measurement and Hierarchical Representations in Early Vision.- 11.4 Biological Research.- 11.5 Machine Research.- Author Index.