A Review on MR Image Intensity Inhomogeneity Correction <s> Bayesian framework <s> Intensity-based classification of MR images has proven problematic, even when advanced techniques are used. Intrascan and interscan intensity inhomogeneities are a common source of difficulty. While reported methods have had some success in correcting intrascan inhomogeneities, such methods require supervision for the individual scan. This paper describes a new method called adaptive segmentation that uses knowledge of tissue intensity properties and intensity inhomogeneities to correct and segment MR images. Use of the expectation-maximization (EM) algorithm leads to a method that allows for more accurate segmentation of tissue types as well as better visualization of magnetic resonance imaging (MRI) data, that has proven to be effective in a study that includes more than 1000 brain scans. Implementation and results are described for segmenting the brain in the following types of images: axial (dual-echo spin-echo), coronal [three dimensional Fourier transform (3-DFT) gradient-echo T1-weighted] all using a conventional head coil, and a sagittal section acquired using a surface coil. The accuracy of adaptive segmentation was found to be comparable with manual segmentation, and closer to manual segmentation than supervised multivariant classification while segmenting gray and white matter. <s> BIB001 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> Bayesian framework <s> 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). <s> BIB002
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