Koenderink J J
Perception. 1984;13(3):321-30. doi: 10.1068/p130321.
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.
本文讨论了一个新定理，该定理将视觉形状的遮挡轮廓的表观曲率与表面的固有曲率和径向曲率联系起来。这个定理允许制定表观曲率的一般规律，而与观察距离无关，并且不管边缘（物体可见部分和不可见部分之间的边界）是一条一般的、因此是扭曲的空间曲线这一事实。因此，视网膜图像中轮廓的凸度、凹度或拐点使观察者能够确定地推断局部表面几何形状。这些结果似乎违反直觉，这从近期作者对该问题的处理中可见一斑。文中展示了一些著名的例子，这些例子过去用于说明轮廓的凹凸与实体形状没有明显关系，但实际上很好地说明了凸度是由于局部卵形形状，凹度是由于局部鞍形形状。
