In this work, a hierarchical graph partitioning based on optimum cuts in graphs is proposed for unsupervised image segmentation, that can be tailored to the target group of objects, according to their boundary polarity, by extending Oriented Image Foresting Transform (OIFT). The proposed method, named UOIFT, theoretically encompasses as a particular case the single-linkage algorithm by minimum spanning tree (MST) and gives superior segmentation results compared to other approaches commonly used in the literature, usually requiring a lower number of image partitions to accurately isolate the desired regions of interest with known polarity. The method is supported by new theoretical results involving the usage of non-monotonic-incremental cost functions in directed graphs and exploits the local contrast of image regions, being robust in relation to illumination variations and inhomogeneity effects. UOIFT is demonstrated using a region adjacency graph of superpixels in medical and natural images.