A graphics rendering system creates an image based on objects constructed of polygonal primitives, which can generate the perception of three-dimensional objects displayed on a two-dimensional display device. An anti-aliasing operation is applied to silhouette edges of the objects, which are the edges of primitives which are displayed at the perimeter of an object. A silhouette edge can be identified by determining how many times an edge is rendered, with each instance of the rendering of an edge corresponding to the rendering of a primitive that adjoins the edge. An edge that is rendered exactly once is interpreted as a silhouette edge. An example of a silhouette edge is an edge that adjoins one triangular primitive that is viewable and another triangular primitive that is hidden from view by other primitives. Another technique for identifying a silhouette edge can be applied to closed objects by determining whether a first primitive adjoining an edge is hidden from view by other primitives and a second primitive also adjoining the edge is viewable. Once the silhouette edges are identified, the anti-aliasing operation is applied thereto.