This paper addresses the issue of bottom-up recovery of structured 2-D geometric primitives from real, complex images. A novel approach for perceptual grouping is presented, using asynchrony whose fundamental principle is to process some primitives before some others, because they carry more information. The main contribution of this work lies in the reduction of the complexity of the grouping process to a problem linear with respect to the number of image contours. Another advantageous characteristic of the proposed method is that only two parameters need to be specified. The asynchronous perceptual grouping processes a data flow of ordered contour primitives, with a rank in the flow determined according to a measure of saliency. It sequentially attempts to group each contour primitive coming in the data flow with other neighboring ones having arrived earlier. Acceptance or rejection of the current contour depends on the geometrical configuration of its neighborhood in the image; properties tested include proximity, colinearity, curvilinearity, and parallelism. The topology as well as the morphology of the relevant structures emerging throughout the whole image are captured in a rigid graph. Junction and surface characteristics are easily extractable, which can help to choose pertinent primitives for an indexing or a recognition system.