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John Wilder, Jacob Feldman, Manish Singh; Contour complexity and contour detectability. Journal of Vision 2011;11(11):1044. doi: 10.1167/11.11.1044.
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Previous work on contour integration has shown that contours with higher curvature are less detectable than those with lower curvature (Field, 1987; Geisler et al., 2001). Contour curvature has also been related to information content, with points of high curvature postulated to carry the most information (Attneave, 1954). This idea was formalized in Feldman and Singh (2005), who expressed the information content, or surprisal, of a contour point as a function of the local turning angle. As a measure of contour complexity, we propose that contour surprisal can be integrated along the length of a contour, yielding a principled measure of cumulative contour complexity. We conducted a series of contour detection experiments to test how the complexity of a contour relates to its detectability. Subjects were shown contours embedded in random monochromatic pixel noise. In a 2IFC task, subjects indicated whether the contour was present in the first or second stimulus. In the first experiment, two contour lengths were tested, with 5 levels of surprisal each. We found a substantial decrease in detectability with increasing contour complexity; while simple (i.e. relatively straight) contours were readily detected, detection of complex (i.e., unpredictably undulating) contours approached chance levels. In a followup experiment, we investigated how the distribution of curvature along the length of the contour influenced detectability; here the results showed independent influences of both local curvature and global contour form. Our approach to contour complexity goes beyond conventional accounts based on simple curvature, because the underlying probabilistic formulation allows global factors to be readily incorporated into the measure. This in turn allows complexity to be quantified in a broader class of contours than is possible in conventional (local) accounts, for example in closed shapes.
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