A method and apparatus for producing water-dominant and fat-dominant MR signal data for use in constructing separate images from single-scan single-point Dixon MRI sequences is disclosed. The effects of field inhomogeneities are removed by quantitating the signal phase by taking the argument of the MR signal multiplied by itself. A region-growing algorithm guided by a polynomial model is used to unwrap the phase which is then used to separately generate water-pixel data and fat-pixel data for producing separate images. The invention can be used for constructing images from both 2-D and 3-D spin-echo and/or field-echo acquisitions.