Eight experiments examined the role of edge-assignment in a contour matching task. Subjects judged whether the jagged vertical edge of a probe shape matched the jagged edge that divided two adjoining shapes in an immediately preceding figure-ground display. Segmentation factors biased assignment of this dividing edge toward a figural shape on just one of its sides. Subjects were faster and more accurate at matching when the probe edge had a corresponding assignment. The rapid emergence of this effect provides an on-line analog of the long-term memory advantage for figures over grounds which Rubin (1915/1958) reported. The present on-line advantage was found when figures were defined by relative contrast and size, or by symmetry, and could not be explained solely by the automatic drawing of attention toward the location of the figural region. However, deliberate attention to one region of an otherwise ambiguous figure-ground display did produce the advantage. We propose that one-sided assignment of dividing edges may be obligatory in vision.