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Daniel Holtmann-Rice, Ohad Ben-Shahar, Steven Zucker; Superposition of Glass Patterns: finding the flow through local measurements. Journal of Vision 2012;12(9):1312. doi: 10.1167/12.9.1312.
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© ARVO (1962-2015); The Authors (2016-present)
The perception of Glass patterns becomes more crisp as the number of correlated dots increases: patterns made from dot pairs reveal a flow, but it is substantially stronger with triples or quadruplets. At first consideration this relationship between pattern and percept seems to be reflected in simple neurobiological mechanisms: Orientationally-selective cells in visual cortex provide (noisy) estimates of the local orientation, which improve as additional correlated dots are added. A simple selection criterion, e.g. winner-take-all, suffices to select the dominant orientation.
The situation becomes more complex when two Glass patterns are superimposed. Superimposing one translational pattern with pairwise dots onto another results in an image perceptually indistinguishable from pure noise. However, with additional correlated dots, the superimposed flows are suddenly revealed. This complex behavior cannot be modeled as easily with the simple mechanism above: winner-take-all can't select multiple values.
Furthermore, the perceptual difference between patterns involving dot pairs as opposed to triples is much greater than that between triples and quadruplets, suggesting a non-linear dependence of percept strength on number of dots.
We have developed an approach to Glass pattern flow inference based on good continuation that models the above perceptual phenomena. As with visual cortex, the computation is organized around orientation hypercolumns. Information implicit within noisy columns of local orientation estimates is supported by neighboring estimates (in both position and orientation). Differential geometry provides the mathematical framework and, as with textures, the flow is controlled by curvature. The model can be implemented via both long-range horizontal and by feedforward/feedback connections.
Experiments with the model show that it properly infers the global flows both in single and superimposed Glass patterns, and that noise is reduced nearly exponentially with additional correlated dots. In effect, the superimposed flows barely interact because of the lift into (position, orientation)-space.
Meeting abstract presented at VSS 2012
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