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Cynthia L. Park, Howard S. Hock, Gregor Schoner; Dynamical model for self-organized pattern formation. Journal of Vision 2001;1(3):370. doi: 10.1167/1.3.370.
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Purpose. A dynamical model of global pattern formation explores the integration of locally detected motions for the directionally ambiguous, counterphase row-of-elements (Hock & Balz, 1994). Pattern formation is bistable for this stimulus; either unidirectional or oscillatory motion patterns are perceived. Small inter-element distances and brief frame durations favor the unidirectional pattern; large inter-element distances and long frame durations favor the oscillatory pattern. Method. The model that reproduces these percepts is based on non-linear dynamical equations that represent: 1) feed-forward contributions of the stimulus to the activation of motion detectors selective to leftward or rightward motion, and 2) contributions of a detector to the activation of other detectors through excitatory and inhibitory interactions that depend non-linearly on the detector's activation level. Results. Inter-element distance influences pattern formation through its feed-forward effect on local motion detector activation. Frame duration influences pattern formation through the time scale of the dynamics and differences in the activation-dependence of excitatory and inhibitory interactions. All the above combine to determine whether the residual activation of leftward vs. rightward detectors at the end of each frame favors motion in the same direction (the basis for the unidirectional pattern) or in the opposite direction (the basis for the oscillatory pattern) during the next frame. Conclusion. There is no need to specify global patterns in a model of global pattern formation. Self-organized motion pattern formation can be accounted for by describing the activation dynamics of local, directionally selective motion detectors.
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