In this work, we propose a hybrid method for seeded image segmentation, named Relaxed OIFT, which extends a method by Malmberg et al. to directed graphs, to properly incorporate the boundary polarity constraint. Relaxed OIFT lies between the pure Oriented Image Foresting Transform (OIFT) at one end and the extension of Random Walks (RW) to directed graphs as proposed by Singaraju et al. Relaxed OIFT is evaluated in MR and CT medical images, producing more intuitively correct segmentation results than both OIFT and RW, and being easy to be extended to multi-dimensional images.