Perceptual representation of visible surfaces

It has long been recognized that a convincing pictorial representation of an object can sometimes be achieved by drawing just a few critical lines. Consider, for example, the photograph of a Henry Moore sculpture that is presented in the left panel of Figure 1 and the line drawing of this object that is presented in the right panel. Although the line drawing leaves out many salient aspects of the photographic image, such as surface color and texture, it effectively conveys the overall three-dimensional (3-D) structure of the depicted scene. Indeed, research has shown that reaction times for recognizing objects from line drawings are no different from the response times obtained for natural photographs (Biederman & Ju, 1988). When an illustrator creates a line drawing of a 3-D scene, the lines are carefully positioned to denote specific landmarks on a surface. One type of landmark to consider in this regard includes the edges that connect planar faces of polyhedral objects. Several such edges from the base of the Moore sculpture are highlighted in Figure 2. Edges are one-dimensional structures and are, therefore, denoted by lines, but there are also important zero-dimensional landmarks (i.e., points) that are often essential for the perceptual interpretation of drawings. Consider, for example, the point labeled a in Figure 2 that marks a vertex where three edges coterminate. There have been numerous mathematical analyses to show how the pattern of vertexes in an image provides potential information about 3-D shape (Clowes, 1971; Draper, 1981; Huffman, 1977; Mackworth, 1973; Malik, 1987; Waltz, 1975a, 1975b), and there is also compelling empirical evidence that these landmarks are a critical source of information for object recognition by human observers (Biederman, 1987). Another type of landmark that is frequently denoted in line drawings includes occlusion contours that define the boundary between visible and occluded regions of a surface. Theoretical analyses have shown that occlusion contours provide potential information about the sign of surface curvature in their immediate local neighborhoods (Koenderink, 1984; Koenderink & van Doorn, 1982b). There is also psychophysical evidence that human observers can exploit that information for the perception of 3-D shape (Koenderink, van Doorn, Christou, & Lappin, 1996) and that it can also be used in the perceptual interpretation of other sources of information, such as shading or texture (Reichel & Todd, 1990; Todd & Reichel, 1989). Occlusion contours are one-dimensional structures that are denoted by lines, but they also contain a variety of salient point structures that could be used as landmarks for human perception. To qualify as a landmark, a contour point must have some salient attribute that makes it stand out from its neighbors. One such attribute is the abrupt termination of a contour at a cusp or T-junction (Koenderink & van Doorn, 1982a; Malik, 1987). Others could be defined by extrema or zero crossings along various dimensions of differential structure. For example, suppose that one was asked to identify the point on a contour that is farthest to the right, such as the one labeled b in Figure 2. Although observers have no difficulty