Edge detection remains an important low-level vision problem. Most edge detection methods operate on an image at a single resolution. Edges within an image, however, generally occur at various resolutions, or scales, and represent transitions of different degrees, or gradient levels. Thus, single-resolution edge detection methods that output binary edge maps do not always yield satisfactory results. We develop a multiresolution (MR) edge detection method based on nonlinear image decomposition that produces gray-level edge maps. Unlike linear decomposition methods that tend to blur image features, nonlinear methods can be designed that yield greater control over the scale of structures preserved by the decomposition. The proposed decomposition method utilizes rank-order-based filtering, which preserves visually important cues, such as edges, while eliminating structures smaller than a minimum constraint. The images produced by the decomposition have progressively lower resolution, or more precisely, contain structures of progressively increasing scale. The resulting sequence of images is subject to an edge detection process that incorporates edge strength to yield gray-level edge maps. These edge maps are restricted to form a stacking edge map pyramid. In this formulation, the base edge map contains edges at all scales, while edge pruning, based on edge scale, is performed at subsequent levels. Thus, moving up in the pyramid yields edge maps with fewer small-scale, or detail, edges. The motivation behind this algorithm comes from tactile imaging, an important problem in facilitating access to visual information for blind people. The proposed scheme is suited for such applications because it provides more control over detail (edge scale) level and is compatible with how the mind perceives information, beginning with course information and progressively increasing the detail level. Simulation results are presented on synthetic signals, electron micrographs, and images. A comparison of results with Park's linear decomposition algorithm demonstrate the advantages of the proposed method.