The perception of three-dimensionality across continuous surfaces

The apparent three-dimensionality of a viewed surface presumably corresponds to several internal preceptual quantities, such as surface curvature, local surface orientation, and depth. These quantities are mathematically related for points within the silhouette bounds of a smooth, continuous surface. For instance, surface curvature is related to the rate of change of local surface orientation, and surface orientation is related to the local gradient of distance. It is not clear to what extent these 3D quantities are determined directly from image information rather than indirectly from mathematically related forms, by differentiation or by integration within boundary constraints. An open empirical question, for example, is to what extent surface curvature is perceived directly, and to what extent it is quantitative rather than qualitative. In addition to surface orientation and curvature, one derives an impression of depth, i.e., variations in apparent egocentric distance. A static orthographic image is essentially devoid of depth information, and any quantitative depth impression must be inferred from surface orientation and other sources. Such conversion of orientation to depth does appear to occur, and even to prevail over stereoscopic depth information under some circumstances.