You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: A Review on MR Image Intensity Inhomogeneity Correction 
Chapter Title:  Bayesian framework 
1. Abstract of Cited Paper (BIB001):  We propose a modification of Wells et al. technique for bias field estimation and segmentation of magnetic resonance (MR) images. We show that replacing the class other, which includes all tissue not modeled explicitly by Gaussians with small variance, by a uniform probability density, and amending the expectation-maximization (EM) algorithm appropriately, gives significantly better results. We next consider the estimation and filtering of high-frequency information in MR images, comprising noise, intertissue boundaries, and within tissue microstructures. We conclude that post-filtering is preferable to the prefiltering that has been proposed previously. We observe that the performance of any segmentation algorithm, in particular that of Wells et al. (and our refinements of it) is affected substantially by the number and selection of the tissue classes that are modeled explicitly, the corresponding defining parameters and, critically, the spatial distribution of tissues in the image. We present an initial exploration to choose automatically the number of classes and the associated parameters that give the best output. This requires us to define what is meant by "best output" and for this we propose the application of minimum entropy. The methods developed have been implemented and are illustrated throughout on simulated and real data (brain and breast MR).

Literature Review:
The Bayes' rule has frequently been employed to estimate the IIH map when the IIH is modeled by a distribution. Let β be a random vector (β 1 , . . . , β n ) with probability density p(β). To estimate β, one can maximize the conditional probability of β given y (the log-transform of x) as follows: This is called the maximum a posterior (MAP) estimate and, by the Bayes rule, is equivalent to Wells et al. BIB001 used the Gaussian distribution to model the entire log-transformed bias field and the observed intensity at voxel i: where Γ i is the tissue class at voxel i with mean value μ(Γ i ), and with ψ x as the covariance matrix. By assuming the statistical independence of voxel intensities and from (7), one can derive When the image data is not polluted by IIH, the above method is simply the tissue classification using a mixture Gaussian model. Hence, this method essentially interleaves the IIH correction with a Gaussian classifier. Guillemaud and Brady BIB002 observed that the effect of IIH correction by Wells et al. algorithm is substantially affected by the Gaussian classifier. In real images, it is very possible for the histogram to deviate from the mixture Gaussian distribution. A modification was then proposed by introducing a tissue class Γ other with a non-Gaussian distribution Zujun Hou