The authors demonstrate that relaxation labelling methods may be rendered effective in the matching of SAR data, provided that more flexible relational models are adopted. The critical ingredient of their method is the use of a hierarchical graph representation of the scene-data and the model. Here the constraints are graded according to their relational power; the more expressive and potentially more fragile perceptual groupings provide the most compatibility constraints while those with the more ambiguous, yet easily recovered, adjacency relations are much weaker. The application vehicle for the study reported in this paper is the matching of hedges detected in SAR images against their cartographic representation in a digital map. The prerequisites for successful matching are the reliable segmentation of the hedge structures and the recovery of a stable relational description suitable for matching against the map data. The former is achieved via the sequential application of a robust intensity ridge detection algorithm and contour grouping prior to the identification of meaningful linear segments. Since linear hedge structures are largely associated with the quadrilateral boundaries of fields, it is parallel and perpendicular groupings of the segments that potentially provide the most perceptual constraints for use in matching. Unfortunately, under conditions of severe noise and clutter, the reliable identification of such groupings is invariably frustrated.