What Does the Occluding Contour Tell Us about Solid Shape?

TLDR

A theorem links the apparent curvature of a shape’s occluding contour to the surface’s intrinsic and radial curvature. The theorem yields general laws for apparent curvature that hold regardless of viewing distance and even when the rim is a twisted space curve. The study shows that retinal contour convexities and concavities reliably reveal local surface geometry—convexities indicate ovoid regions and concavities indicate saddle regions—contrary to prior intuition.

Abstract

A new theorem is discussed that relates the apparent curvature of the occluding contour of a visual shape to the intrinsic curvature of the surface and the radial curvature. This theorem allows the formulation of general laws for the apparent curvature, independent of viewing distance and regardless of the fact that the rim (the boundary between the visible and invisible parts of the object) is a general, thus twisted, space curve. Consequently convexities, concavities, or inflextions of contours in the retinal image allow the observer to draw inferences about local surface geometry with certainty. These results appear to be counterintuitive, witness to the treatment of the problem by recent authors. It is demonstrated how well-known examples, used to show how concavities and convexities of the contour have no obvious relation to solid shape, are actually good illustrations of the fact that convexities are due to local ovoid shapes, concavities to local saddle shapes.