Image curves often correspond to the bounding contours of objects as they appear in the image. As such, they provide important structural information which may be exploited in matching and recognition tasks. However, these curves often do not appear as coherent events in the image; they must, therefore, be (re)constructed prior to their effective use by higher-level processes. A system (currently being built) to accomplish such reconstruction of image curves is described herein. It exploits principles of perceptual organization such as proximity and good continuation to identify co-curving or curvilinear structure. Components of each such structure are replaced by a single curve, thus making their coherence explicit. The system is iterative, operating over a range of perceptual scales--fine to coarse--and yielding a hierarchy of alternative descriptions. Results are presented for the first iteration, showing the performance of the system at the finest perceptual scale and indicating the reasonableness of the paradigm for subsequent iterations.