An outline drawing often serves as an excellent depiction of a visual scene. Somehow, our visual system can form two- and three-dimensional percepts solely from one-dimensional contour information. In mathematics, contour closure plays a key role in bridging this dimensional gap, however in perception the link between closure and shape is unclear. To better understand this relationship, we devised a set of visual search experiments in which subjects discriminate outline figures by means of their two-dimensional shape. By modulating the degree of closure of the outlines, we show that two-dimensional shape processing is rapid for closed stimuli but slow for open stimuli. We further show that search can be characterized as a smooth, monotonie function of the degree of closure, supporting the notion of a perceptual closure continuum.