This paper proposes a new solution for local binary fitting energy minimization based on graph cuts for automatic brain structure segmentation on magnetic resonance images. The approach establishes an effective way to embed the energy formulation into a directed graph, such that the energy is minimized by maximizing the graph flow. Proposed and conventional solutions are compared by segmenting the well-known BrainWeb synthetic brain Magnetic Resonance Imaging database. Achieved results show an improvement on the computational cost (about 10 times shorter) while maintaining the segmentation accuracy (96%).