Retrospective Evaluation and Correction of Intensity Inhomogeneity - Advance Image Processing in Magnetic Resonance Imaging - page 152

update inhomogeneity

classify

update Gaussian distributions

FIGURE 5.4 Rather than using a manually trained classifier, as Wells et al., do, Van
Leemput et al., automatically train the classifier during the iterative EM procedure. The
resulting three-step algorithm adapts to each individual scan to be analyzed, allowing to
process images obtained with a variety of acquisition protocols without user intervention.

which simply states that the updated mean and variance estimations for class are
given by the sample mean and sample variance of the inhomogeneity-corrected
intensities of voxels classified as tissue type k .
To summarize, the algorithm of Van Leemput et al. iteratively alternates
between tissue classification, inhomogeneity field estimation, and retraining of the
classifier (see Figure 5.4). The iterative scheme is initialized by setting the inho-
mogeneity field coefficients to zero (no inhomogeneity) and providing a first rough
estimate of the tissue-class probabilities p ik , allowing start of the iterative EM
scheme with the Gaussian distribution parameter estimation step. The initial class
probability estimates are given by prealigning the image under study with a so-
called atlas that contains information about the expected location of the tissue types
of interest in a normal population. The alignment is performed fully automatically
by maximizing the mutual information [31,32] between the image under study and
an anatomical template associated with the atlas, which works irrespective of the
tissue characteristics in the images. Because the classifier is additionally trained
automatically, images acquired with a previously unseen MR sequence can readily
be analyzed without requiring user intervention. Van Leemput et al. originally
applied their method to brain MRI,* but Lorenzo-Valdés et al. recently extended
the technique to analyze 4-D cardiac MR images [33]. A similar algorithm for brain
MRI was developed independently by Ashburner et al.** working on the original
MR intensities rather than on log-transformed intensities, and using a linear

k

* The software of Van Leemput et al. is freely available under the name EMS (expectation-maximization

segmentation) at http://www.medicalimagecomputing.com/EMS
** Freely available as part of the SPM99 package at http://www.fil.ion.ucl.ac.uk/spm/spm99.html .