Ok now this is all mathematical hope this helps.
https://www.google.co.nz/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCsQFjAA&url=http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F12926119_MRI_geometric_distortion_a_simple_approach_to_correcting_the_effects_of_non-linear_gradient_fields%2Ffile%2F60b7d515a7b5389c97.pdf&ei=EnNXU5PRD8ahkAWvpYG4CA&usg=AFQjCNFPCYgCsjmmBPsoAv_-uV5PbKGt0g&sig2=R8c2sSeGxJTsJyqY8C80Xg&bvm=bv.65177938,d.dGI
i've done some (unpublished) research on correction of slow varying multiplicative bias MRI correction of brain imaging algorithms a while ago. If we consider coefficient of variation within a single tissue type like white or gray matter, to be an adequate quality metric, then EM algorithms that work in conjunction with segmentation (e.g. FSL FAST) appear to outperform polynomial fits.
see
C.P. Loizou, M. Pantziaris, C.S. Pattichis, I. Seimenis, “Brain MRI Image normalization in texture analysis of multiple sclerosis”, J. Biomed. Graph. & Comput., vol. 3, no.1, pp. 20-34, 2013.
The first step to avoid as much distortion as possible is to use an appropriate standard template when normalizing the brains. For example, when normalizing brains of older adults who have experienced stroke, I used the Clinical Toolbox in SPM8 that has a template brain from older adults, which was more suitable for my sample. There would be severe distortion if you were to attempt to normalize using a healthy young adult standard template, such as an MNI brain.
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