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Guy Ben-Yosef, Ohad Ben-Shahar; Neural patterns of minimal bending as perceptual curve completion. Journal of Vision 2012;12(9):880. doi: https://doi.org/10.1167/12.9.880.
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© ARVO (1962-2015); The Authors (2016-present)
Visual curve completion is a fundamental perceptual organization process which attracts studies in both biological and machine vision research. Recent studies suggested framing the completion process directly in the visual area where presumably a significant part of it occurs, namely, the primary visual cortex. It was hypothesized that the perceived completed curves are formed by V1 neural activation patterns that obey certain biological and/or physical energy criteria. Since a suitable mathematical abstraction for V1 is the tangent bundle space R^2 x S^1, such energy criteria of neural activation patterns can be conveniently explored via formal energies of curves in this space.
While previously it has been suggested to investigate the energy determined by the mere number of active cells in the pattern (which amounts to the pattern that consumes the minimal energy, e.g., Ben-Yosef&Ben-Shahar 2010), here we suggest considering also the properties of horizontal connectivity in V1. We show that patterns in which similarity between consecutive links is optimized, may be abstracted as curves of minimum bending (or curvature) in the tangent bundle space (i.e., elastica in the tangent bundle). Putting into action this basic (and single) principle provides completion predictions that match many psychophysical findings. Perhaps the most interesting one is that information of boundary curvature at the point of occlusion is both necessary and significant for a completion solution, in accordance with old and recent empirical and theoretical reports (e.g., Takeichi 1995; Singh&Hoffman 1999; Singh&Fulvio 2005). Based on this principle, we implement a numerical shape completion algorithm which (to the best of our knowledge) is the first ever to explicitly use boundary curvature in addition to boundary orientation and position. We show various experimental results which demonstrate the advantage of using boundary curvature for predicting perceptual completions and contours in natural scenes.
Meeting abstract presented at VSS 2012
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