The spatiotemporal analysis of deforming silhouettes (apparent contours) is here extended using the mathematics of perspective projections and tools from differential geometry. Analysis of the image motion of a silhouette or apparent contour enables computation of local surface curvature along the corresponding contour generator on the surface, assuming viewer motion is known. To perform the analysis, a spatiotemporal parameterization of image-curve motion is needed, but is underconstrained (a manifestation of the well-known aperture problem). It is shown that an epipolar parameterization is most naturally matched to the recovery of surface curvature.