||There are several well known segmentation algorithms which outputs optimize the $\ell_p$ norms of associated graph cuts.
However, so far, such optimizations were restricted only to the cases, when graphs associated with the images were undirected graphs.
In this talk, we discuss the situation when such optimization can be extended to directed graphs setting. This facilitates
an incorporation of image orientedness properties into the segmentation process. Moreover, we describe how this oriented set-up
can be efficiently applied to the multi-object segmentation, when the inclusions/disjointness hierarchy among the objects is known.