This paper describes a method for finding wide-baseline correspondences between images at locations along gradient edges. We find edges in scale space using established methods and develop invariant descriptors for these edges based on orientation and scale histograms. Because edges are often found on occluding boundaries, we calculate and store two descriptors per edge, one on each side, for robustness to occlusions. We demonstrate the effectiveness of edge matching in the applications of wide-baseline correspondence, structure from motion from line segments, and object category recognition on the Caltech 101 dataset.