1. A computer readable medium embodying instructions executed by a processor to perform a method for image volume segmentation, the method steps comprising: receiving an input image; forming a primal 6-connected lattice of edges and a dual 6-connected lattice of faces defining an object in the input image, wherein the faces in the dual 6-connected lattice correspond to edges in the primal 6-connected lattice, wherein the edges in the primal 6-connected lattice connect voxels of the input image; obtaining one or more oriented closed contours on respective slices of the input image; defining a face weight for each of the faces of the dual 6-connected lattice based on a function of image intensities of the voxels of a corresponding edge; identifying a surface of the input image having an initial boundary based on the face weights; determining a three-dimensional minimum-weight surface including the initial boundary as a set of saturated edges in the primal 6-connected lattice of edges corresponding to a minimum-cost circulation network flow, wherein the minimum-weight surface is a three-dimensional segmentation of a portion of the object with the one or more oriented closed contours defining a boundary of the three-dimensional minimum-weight surface determination; and outputting the three-dimensional minimum-weight surface as a segmentation of the input image.