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i've done some (unpublished) research on correction of slow varying multiplicative bias MRI correction of brain imaging algorithms a while ago.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.
The image normalisation should be made by taking into consideration, information from the same slice and the neighbohring slices. This is taken is taken from the black and white matter areas of the brain. By normalising the image i.e. the image histogram, we are making the images able to be compared with each other. That is considerably usfull in the case of tumour deliniations, when measuring for exmple the size of a tumour and we are interested for exact measurements. More importantly when texture features and other information is extracted from areas of the brain from images taking at different time points (i.e. from neighbohring brain slices) then the images should be normalised so that the extracted features can be comparable. Otherwise the comparison dosenot make any sence. In our publication above we do propose the most appropriate normalisation method/s (by comparing 5 different methods) for the MRI brain images. The SPM8 is good but it is not application specific and dosenot take into considerartion the chnages of the black and white matter in each slice.
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