Water/fat separation is a classical problem for in vivo proton MRI. Although many methods have been proposed to address this problem, robust water/fat separation remains a challenge, especially in the presence of large amplitude of static field inhomogeneities. This problem is challenging because of the nonuniqueness of the solution for an isolated voxel. This paper tackles the problem using a statistically motivated formulation that jointly estimates the complete field map and the entire water/fat images. This formulation results in a difficult optimization problem that is solved effectively using a novel graph cut algorithm, based on an iterative process where all voxels are updated simultaneously. The proposed method has good theoretical properties, as well as an efficient implementation. Simulations and in vivo results are shown to highlight the properties of the proposed method and compare it to previous approaches. Twenty-five cardiac datasets acquired on a short, wide-bore scanner with different slice orientations were used to test the proposed method, which produced robust water/fat separation for these challenging datasets. This paper also shows example applications of the proposed method, such as the characterization of intramyocardial fat. Magn Reson Med, 2010. © 2009 Wiley-Liss, Inc.