Seed-based methods for region-based image segmentation are known to provide satisfactory results for several applications, being usually easy to extend to multidimensional images. However, while boundary-based methods like live wire can easily incorporate a preferred boundary orientation, region-based methods are usually conceived for undirected graphs, and do not resolve well between boundaries with opposite orientations. This motivated researchers to investigate extensions for some region-based frameworks, seeking to better solve oriented transitions. In this same spirit, we discuss how to incorporate this orientation information in a region-based approach called "IFT segmentation by seed competition" by exploring digraphs. We give direct proof for the optimality of the proposed extensions in terms of energy functions associated with the cuts. To stress these theoretical results, we also present an experimental evaluation that shows the obtained gains in accuracy for some 2D and 3D data sets of medical images. © 2013 IEEE.