Dynamic neural field theory for motion perception

1 Introduction.- I Basic Concepts.- 2 Visual perception of motion.- 2.1 Apparent Motion (AM).- 2.2 Motion Energy Models.- 2.3 Motion Correspondence Problem.- 2.4 Cooperativity in Motion Perception.- 2.5 Motion Perception as Regularization Problem.- 2.6 Motion Perception as Statistical Optimization Problem.- 2.7 Motion Perception as Dynamical Process.- 2.8 Motion Transparency.- 2.9 Adaptation.- 2.10 Summary.- 3 Basic principles of the dynamic approach.- 3.1 Central Idea.- 3.2 Behavioral Variables.- 3.3 Behavioral Dynamics.- 3.4 Stability.- 3.5 Bifurcations.- 3.6 Intrinsic Dynamics and Behavioral Information.- 3.7 Comparison between Theory and Experiment.- 3.8 Summary.- 4 Dynamic neural fields.- 4.1 Biological Motivation.- 4.2 Generalization by the Dynamic Approach.- 4.3 Amari Model: Intuitive Concepts.- 4.3.1 Field without Interaction.- 4.3.2 Field with Linear Interaction.- 4.3.3 Neural Field with Constant Input.- 4.3.4 Neural Field with Slightly Varying Input.- 4.4 Amari Model: Mathematical results.- 4.5 Summary.- II Model for Motion Perception.- 5 Dynamic neural field model for motion perception.- 5.1 Perceptive Space.- 5.2 Neural Activation Field.- 5.3 Dynamical State and Stability.- 5.4 Specification by the Stimulus.- 5.5 Cooperativity.- 5.6 Fluctuations.- 5.7 Adaptation.- 5.8 General Neural Field Model.- 5.9 Summary.- 6 Necessity of the concepts: Model for the motion quartet.- 6.1 Dynamical Model for the Motion Quartet.- 6.1.1 Perceptive Space, Activation Dynamics, and Fluctuations.- 6.1.2 Cooperativity.- 6.1.3 Adaptation.- 6.2 Experimental and Numerical Methods.- 6.3 Necessity of State and Stability.- 6.3.1 Necessity of Perceptual State.- 6.3.2 Necessity of (Multi-)Stability.- 6.4 Necessity of Fluctuations and Adaptation.- 6.4.1 Necessity of Fluctuations and Their Interaction with Stability.- 6.4.2 Necessity of Adaptation.- 6.4.3 Necessity of Activation as Dynamical State Variable.- 6.4.4 Relative Importance of Fluctuations and Adaptation.- 6.5 Discussion.- 6.6 Summary.- 7 Sufficiency of the concepts: Field model for 2D-motion perception.- 7.1 Implementation of the Neural Field Model.- 7.1.1 Neural Field Dynamics, Fluctuations, and Adaptation.- 7.1.2 Specifying Influence of the Stimulus.- 7.1.3 Interaction Function.- 7.1.4 Activity Dependent Scaling of the Interaction Function.- 7.1.5 Numerical Methods.- 7.2 Results: Integration of Multiple Functionalities.- 7.2.1 Spatio-Temporal Integration and Prediction.- 7.2.2 Solution of the Motion Correspondence Problem.- 7.2.3 Smoothing and Active Segmentation.- 7.2.4 Motion Transparency.- 7.3 Balance between Stimulus and Cooperativity.- 7.4 Discussion.- 7.5 Summary.- 8 Relationships: neural fields and computational algorithms.- 8.1 Lyapunov Functions.- 8.2 Lyapunov Functional.- 8.3 Relationship: Neural Fields and Regularization Approaches.- 8.4 Probabilistic Interpretation of Neural Fields.- 8.5 Neural Fields as Robust Estimators.- 8.6 Prediction Properties of the Neural Field.- 8.7 Summary and Discussion.- 9 Identification of field models from neurophysiological data.- 9.1 Estimation of Behavior Related Quantities from Neural Responses.- 9.2 Description of the Algorithm.- 9.2.1 Neurophysiological Data.- 9.2.2 Reconstruction of the Activation Distribution.- 9.2.3 Estimation of the Neural Field Parameters.- 9.3 Results.- 9.4 Discussion and Outlook.- 9.5 Summary.- III Other Applications of Neural Fields.- 10 Neural field model for the motor planning of eye movements.- 10.1 Basic Experimental Phenomenology.- 10.2 Neural Field Model.- 10.2.1 Neural Field for the Representation of the Motor Plan.- 10.2.2 Cooperative Interaction.- 10.2.3 Specifying Input.- 10.2.4 Output Stage.- 10.3 Examples for Reproduced Experimental Effects.- 10.3.1 Averaging and Decision Making.- 10.3.2 Bias by Statistical a Priori Information.- 10.3.3 Effect of Warning Signals.- 10.4 Discussion.- 10.5 Summary.- 11 Technical applications of neural fields.- 11.1 Path Planning for an Autonomous Robot.- 11.1.1 System Architecture.- 11.1.2 Results.- 11.2 Integration of Visual Representations.- 11.2.1 System Architecture.- 11.2.2 Results.- 11.3 Computationally Efficient Implementations.- 11.4 Discussion.- 11.5 Summary.- 12 Discussion.- 12.1 Aspects Concerning the Model for Motion Perception.- 12.2 Aspects Concerning other Applications of Neural Fields.- Appendices.- A Appendix of chapter 3.- A.1 Relationship: Eye-Position and Relative Phase Dynamics.- B Appendix of chapter 6.- B.1 Geometry Dependence of Feed-Forward Input.- B.2 Stochastic Bistable Dynamics.- B.3 Parameters of the Model for the Motion Quartet.- C Appendix of chapter 7.- C.1 Properties of the Interaction Function.- C.2 One-Dimensional Neural Field Model for Motion Direction.- C.3 Parameters of the Neural Field Model.- D Appendix of chapter 8.- D.1 Proof of Theorem 4.- D.2 Proof of Lemma 1.- D.3 Proof of Theorem 5.- E Appendix of chapter 9.- E.2 Least Squares Estimation of Kernel Functions.- E.3 Equivalent Feed-Forward System for a Linear Threshold.- F Appendix of chapter 11.- F. 1 Transformation between Robot and World Coordinates.- F.2 Transformations between the Perceptive Spaces.- F.3 Learning of the Parameters of the Approximation Dynamics.- List of Symbols.