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Guy Ben-Yosef, Ohad Ben-Shahar; Tangent bundle contour completion with early vision mechanisms. Journal of Vision 2011;11(11):1036. doi: 10.1167/11.11.1036.
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© ARVO (1962-2015); The Authors (2016-present)
Visual contour completion is a classical vision problem which has been explored for over a century. Efforts to model the shape of the completed contour has been made in the past decades mainly in an “axiomatic” fashion, i.e., by predefining a set of “desired” perceptual/geometrical properties (e.g. minimum total curvature in Ulman, 1976; Mumford, 1994, or minimum total change of curvature and roundedness in Kimia, 2003) and then seeking the curve that satisfies them. However, some of these perceptual axioms are debatable (e.g. roundedness in Singh & Fulvio, 2005, scale invariance in Gerbino & Fantoni, 2006) and some of them are difficult to measure psychophysically.
Recently, we suggested to model the shape of the competed contour from the perspective of the primary visual cortex while using its abstraction as the unit tangent bundle space R2 × S1. Curves in this space represent the activation pattern of orientation selective cells due to real or completed image contours, and the pattern of fewest active cells (i.e. the curve of minimal length) is sought for, assuming the completion mechanism aspires for a minimum energy state (Ben-Yosef & Ben-Shahar, 2010). While previously we proposed a rigorous mathematical analysis for this principle and an exploration of its derived visual properties, here we propose a biologically-plausible mechanism and computational model for the computation of the corresponding completed curve with known early visual mechanisms. We then present results of our model in comparison to reported completions by human observers (e.g., Fulvio et al., 2008) and show how they match with unprecedented accuracy to support our curve completion theory.
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