A computational framework for computing curvilinear structure on the edge data of images is presented. The method is symbolic, operating on geometric entities/tokens. It is also constructive, hierarchical, parallel, and locally distributed. Computation proceeds independently at each token and at each stage interleaves the discovery of structure with its careful description. The process yields a hierarchy of descriptions at multiple scales. These multiscale descriptions provide efficient feature indexing both for the grouping process itself as well as for subsequent recognition processes. Experimental results are presented to demonstrate the effectiveness of the approach with respect to curvilinear structure, and its application to more general grouping problems is discussed.>