The speed of contour integration was investigated in a task that can be solved by grouping contour segments into elongated curves. Subjects had to detect a continuous curve, which could be intersected by one or two other curves. At locations where these curves came in close proximity, the assignment of contour segments to the different curves could be based on collinearity. Reaction times exhibited a strong dependence on (1) the presence of intersections among curves; and (2) the context provided by the stimulus set from which individual stimuli were selected. Reaction times were shortest when grouping of contour segments depended on information at a single location in the visual field. In this condition, responses to stimuli containing an intersection were faster than responses to stimuli that did not. When responses were determined by information at spatially separate locations, responses were delayed, and every intersection increased the reaction time considerably. This result contrasts with earlier investigations which have suggested that contour integration on the basis of collinearity is performed pre-attentively but is in accordance with studies on curve tracing. We propose that the assignment of contour segments to equally coherent curves, a process which may be called figure-figure segregation, is a function of object-based attention. Moreover, the protracted reaction times for some of the stimuli indicate that spread of attention within an object costs time. This implies that object recognition is not always as fast as is sometimes assumed.