Surface geometry influences the shape of illusory contours.

Geometric and neural models of illusory-contour (IC) synthesis currently use only local contour geometry to derive the shape of ICs. Work on the visual representation of shape, by contrast, points to the importance of both contour and surface geometry. We investigated the influence of surface-based geometric factors on IC shape. The local geometry of inducing-contour pairs was equated in stereoscopic IC displays, and the shape of the enclosed surface was varied by manipulating sign of curvature, cross-axial shape width, and medial-axis geometry. IC shapes were measured using a parametric shape-adjustment task (Experiment 1) and a dot-adjustment task (Experiment 2). Both methods revealed large influences of surface geometry. ICs enclosing locally concave regions were perceived to be systematically more angular than those enclosing locally convex regions. Importantly, the influence of sign of curvature was modulated significantly by shape width and medial-axis geometry: IC shape difference between convex and concave inducers was greater for narrow shapes than wider ones, and greater for shapes with straight axis and symmetric contours (diamond versus bowtie), than those with curved axis and parallel contours (bent tubes). Even at the level of illusory "contours," there is a contribution of region-based geometry which is sensitive to nonlocal shape properties involving medial geometry and part decomposition. Models of IC synthesis must incorporate the role of nonlocal region-based geometric factors in a way that parallels their role in organizing visual shape representation more generally.