Retrospective Evaluation and Correction of Intensity Inhomogeneity - Advance Image Processing in Magnetic Resonance Imaging - page 158

time series of the same subject. For example, PABIC was used as a required
preprocessing step for a method developed at ETH Zürich to segment and charac-
terize multiple sclerosis lesions based on dynamic changes over time [51].

Figure 5.1 shows the results of a MR inhomogeneity correction using PABIC.

PABIC cannot only be applied to MR images but to any kind of image data satisfying
the initial assumptions of piecewise constant intensity regions. The algorithm was
tested successfully on different kinds of microscopy images and biological scenes
measured by a video camera.

5.4.2 I NFORMATION M INIMIZATION AND N3

The methods discussed in this section do not require any explicit model of the
intensities or the spatial distributions of the different classes present in an MR
image. This property stabilizes the correction method against pathological inten-
sity distributions in MR data that might violate the class model. Known intensity
pathologies, such as multiple sclerosis lesions in brain MR images, are handled
without adaptions.
Paul Viola [52] was the first to propose in his Ph.D. thesis the use of a criterion
based on information theory. He proposed to minimize the information content
of the histogram. Other image processing applications such as image restoration
and classification have successfully employed information minimization. The
information I of an image z can be quantitatively computed using the Shannon
entropy H ( z ) as

∑

I z () = H z () = − pi ()log () ⋅ pi (5.19)

i

with p ( n ) denoting the probability that an element of image z has intensity i . The
value of H ( z ) is positive and H ( z ) is maximal when all intensities have the same
probability. Thus, the main assumption of the information minimization approach
is that the histogram shows thin “spiky” unimodal intensity distributions. If this
assumption is satisfied, then the information of a perfect MR image is minimal.
Intensity inhomogeneities in the MR image result in spreading the class distri-
butions, leading to a more uniform histogram with higher information content.
The information minimization idea was then picked up by several researchers
such as Mangin [18], Likar et al. [53], and many more.* Mangin models a multi-
plicative inhomogeneity field using B-splines, whereas Likar's method incorporates
both a multiplicative and an additive inhomogeneity field using orthonormal poly-
nomial basis functions. Likar's method is currently probably the most versatile
histogram-based method.
Based on similar assumptions, John Sled [54,55] proposed another histogram-
sharpening approach called nonparametric, nonuniform intensity normalization

* The SPM2 package freely available at http://www.fil.ion.ucl.ac.uk/spm/spm2.html contains an

implementation of intensity inhomogeneity correction via information minimization.