1. A computer readable medium embodying instructions executable by a processor to perform a method for image volume segmentation, the method steps comprising: receiving an input image; obtaining an oriented closed contour on one or more slices of the input image; defining face weights from the input image; identifying a surface having a desired boundary based on the face weights; determining a minimum-cost circulation through the surface; determining a minimum-weight surface having the boundary as a set of saturated edges in a primal graph corresponding to faces, given by the oriented closed contour and the minimum-cost circulation; and outputting the minimum-weight surface as a segmentation of the input image.