Contour curvature polarity and surface interpolation

Abstract

Contour curvature polarity (i.e., concavity/convexity) is recognized as an important factor in shape perception. However, current interpolation models do not consider it among the factors that modulate the trajectory of amodally-completed contours. Two hypotheses generate opposite predictions about the effect of contour polarity on surface interpolation. Convexity advantage: if convexities are preferred over concavities, contours of convex portions should be more extrapolated than those of concave portions. Minimal area: if the area of amodally-completed surfaces tends to be minimized, contours of convex portions should be less extrapolated than contours of concave portions. We ran three experiments using two methods, simultaneous length comparison and probe localization, and different displays (pictures vs. random dot stereograms). Results indicate that contour polarity affects the amodally-completed angles of regular and irregular surfaces. As predicted by the minimal area hypothesis, image contours are less extrapolated when the amodal portion is convex rather than concave. The field model of interpolation [Fantoni, C., & Gerbino, W. (2003). Contour interpolation by vector-field combination. Journal of Vision, 3, 281-303. Available from http://journalofvision.org/3/4/4/] has been revised to take into account surface-level factors and to explain area minimization as an effect of surface support ratio.

Visual Representation of Contour and Shape

“…First, illusory contours enclosing locally concave shapes were found to be systematically more angular (closer to the intersection point of the linear extrapolations of the two inducers) than those enclosing locally convex shapes. This influence of local convexity is consistent with results obtained with partly occluded shapes (Fantoni et al, 2005). Beyond the influence of local sign of curvature, however, this influence of local convexity also exhibited an interaction with two skeleton-based variables: shape width and axis curvature.…”

The “side” matters: How configurality is reflected in completion

“…Since the proposed spatial integration propagates activation along straight pathways, an occluded angle should be always perceived as having a sharp vertex. This is contradicted by several empirical findings showing that the shape of interpolated angles is a smooth compromise between the sharp vertex solution and the straight connection between endpoints (e.g., Fantoni, Bertamini, & Gerbino, 2005). Finally, the DISC model seems unsuitable to explain the dependence of the precise shape of the interpolated path from variables like completion type (modal vs. amodal;Singh, 2004), occlusion symmetry , retinal gap size (Gerbino & Fantoni, 2006), and orientation (Fantoni, Sgorbissa, & Gerbino, 2001).…”

Processing convexity and concavity along a 2-D contour: figure–ground, structural shape, and attention

“…Using this technique, they concluded that convexity is a strong factor that groups two regions together. Fantoni, Bertamini, and Gerbino (2005) found that the extent of amodal completion of a partly hidden surface Fig. 3 The piecewise convexity of the shape in the examples determines the perception of that region as figure.…”

“…For convex contours (left), grouping was stronger, and consequently, there was a tendency to perceive the two figural elements as coplanar, making the task of adjusting relative depth harder. Bottom: Illustration of the stimuli used in one of the experiments by Fantoni et al (2005) to compare amodal completions of shapes. The small hexagon in front was the occluder, and the partly occluded contours had convex or concave vertices.…”