Inferring 3D surface shape from 2D contour curvature

Boundary shape alone (e.g. in silhouettes) can be a strong perceptual cue to the 3D shape of a smooth object. Certainly the sign of curvature of the bounding contour strongly constrains the 3D shape of the surface at the rim: convex points on the boundary project from convex surface points, whereas concave points project from surface saddle points (Koenderink & van Doorn 1976; Koenderink 1984). Furthermore, when curvature changes smoothly over the surface of an object, these boundary constraints may also carry information about the qualitative shape of the 3D surface interior to the boundary. Here we ask whether the magnitude of curvature of the bounding contour might also contribute to the perceived 3D shape on the interior surface of an object. We generated random 3D shapes by adding Perlin noise to spheres. Objects were partially occluded such that a wedge segment of the object was visible. In separate trials, the bounding contour was either visible or occluded. Observers adjusted the depth of a binocularly viewed dot so that it was perceived to lie on the surface. We found that when direct surface shading and disparity cues were weak, the perceived surface shape on the interior of the object was modulated by the magnitude of curvature of the bounding contour. When direct cues to surface shape were strengthened, this boundary effect was substantially reduced. We conclude that the influence of the bounding contour on the perception of 3D object shape derives not just from the sign of curvature but also its magnitude. We discuss this finding in terms of the ecological statistics of 3D curvature and projected contours of objects in our visual environment.