1. A method of separating and identifying water and fat magnetic resonance (MR) images using an MRI apparatus, comprising the steps of: a) obtaining nuclear magnetic resonance (NMR) image data from at least a first MR echo signal (S 1 ) and a second MR echo signal (S 2 ), where water and fat signals are orthogonal in the first MR echo signal and water and fat signals are either parallel or anti-parallel in the second MR echo signal; b) obtaining a field map of background main magnetic field (P) from the second MR echo signal by applying a seed-guided phase unwrapping algorithm to the image data obtained from the second MR echo signal according to 11 P = 1 2 &it; λ &it; unwrap &it; { arg &af; ( S 2 × S 2 ) } ; c) removing the effect of background field inhomogeneties according to the unwrapped field map to yield a corrected first MR echo signal (S 1 ′) and a corrected second MR echo signal (S 2 ′); d) calculating an intermediate data for the corrected first MR echo signal according to sequence parameters of data acquisition; e) summing an imaginary portion of the intermediate data; f) distinguishing whether a seed reference used in applying the phase unwrapping is water-dominant or fat-dominant based on the polarity of the sum of the imaginary portion of the intermediate data, and g) determining water and fat images from the corrected first and second MR echo images based on whether the seed reference is water-dominant or fat-dominant.