Directional decomposition of maps and line-drawing images has the advantage of stressing directional information, and so may assist in the analysis of such images. In this paper, a method is described for directional decomposition of maps and line-drawing images into an arbitrary number of directional edge planes, where the range of directions that is included in each directional edge plane may be determined individually. The proposed approach is based on self dilated line kernels, which are generated by dilating discrete periodic line segments by themselves. These kernels are then used by regulated morphological operations, that extend the fitting interpretation of the ordinary morphological operations, in order to obtain the required decomposition. The paper describes necessary propositions of the proposed approach, and represents examples of their use for the application of line-drawings analysis.