1. A computerized method for generating a phase corrected magnetic resonance image or images comprising: (a) acquiring a magnetic resonance image or images containing background or error phase information; (b) calculating two vector images A and B using the acquired image or images so that a vector orientation by one of the two vector images at a pixel is substantially determined by the background or error phase at the pixel, and the vector orientation at the pixel by the other vector image is substantially different from that determined by the background or error phase at the pixel; (c) applying a sequenced region growing phase correction algorithm to the vector images A and B to construct a new vector image V, wherein the algorithm comprises: (i) selecting an initial seed pixel or pixels and assigning either A or B of the initial seed pixel or pixels as a value of V for the initial seed pixel or pixels; (ii) selecting a secondary seed pixel and selecting either A or B of the secondary seed pixel as a value of V for the secondary seed pixel based on whether A or B of the secondary seed pixel has a smaller angular difference with an estimated V for the secondary seed pixel; (iii) determining for the secondary seed pixel a local quality metric for each of the nearest neighbor pixels of the secondary seed pixel for which V has not been determined and assigning a priority to each of the nearest neighbor pixels using the local quality metric in order to determine the sequence by which each of the nearest neighbor pixels is to be selected as a further seed pixel; (iv) repeating the steps of (ii) and (iii) to complete the sequenced region growing with respect to further seed pixels and to construct the vector image V so that a vector orientation of V at each pixel is substantially determined by the background or error phase at the pixel; (d) generating the phase corrected magnetic resonance image or images from the acquired magnetic resonance image or images using the vector image V; and (e) displaying or archiving the phase corrected magnetic resonance image or images, and further comprising correcting vector images A and B with a global linear error phase correction in one or more dimensions prior to performing the sequenced region growing.