Inhomogeneity Correction

• Scans can have nonuniform intensities throughout the brain
• Usually low frequency - smooth over the brain (assumed)
• Referred to as bias, bias field, or inhomogeneity

Image From https://www.slicer.org/w/images/7/77/MRI_Bias_Field_Correction_Slicer3_close_up.png

It’s hard to see subtler bias fields, but sometimes they can be seen visually.

ortho2(robust_window(t1))

flair = neurobase::readnii("training01_01_flair.nii.gz")
ortho2(robust_window(flair))

image(robust_window(t1), useRaster = TRUE)

We will use N4: Improved N3 Bias Correction (Tustison et al. 2010).

The model assumed in the N4 is: $$v(x) = u(x)f(x) + n(x)$$

• $v$ is the given image
• $u$ is the uncorrupted image
• $f$ is the bias field
• $n$ is the noise (assumed to be independent and Gaussian)
• $x$ is a location in the image

The data is log-transformed and assuming a noise-free scenario, we have:

$$\log(v(x)) = \log(u(x)) + \log( f(x) )$$

• N4 uses a B-spline approximation of the bias field
• It iterates until a convergence criteria is met
  • when the updated bias field is the same as the last iteration
• It outputs the data back in the original units (not log-transformed)

Here we will use the bias_correct function in extrantsr, which calls n4BiasFieldCorrection from ANTsR.

You can pass in the image:

library(extrantsr)
bc_t1 = bias_correct(file = t1, correction = "N4")

or the filename (but negatives are in there):

bc_t1 = bias_correct(file = "training01_01_t1.nii.gz", correction = "N4")

Here we take the ratio of the images and overlay it on the original image:

ratio = t1 / bc_t1; ortho2(t1, ratio)

We are breaking the ratio into quantiles:

ortho2(t1, ratio, col.y = colors, ybreaks = quantiles, ycolorbar = TRUE)

• Inhomogeneity correction is one of the first steps of most structural MRI pipelines
• Inhomogeneity can cause problems for other methods/segmentation
• Corrections try to make tissues of the same class to have similar intensities
• Use the extrantsr bias_correct function
  • There is also fsl_biascorrect from fslr (not as effective in our experience)
• You may also want to run corrections after skull stripping on the brain only
  • this is possible with the result after the brain extraction lecture
  • correction before skull-stripping may be necessary and can improve after correction

http://johnmuschelli.com/imaging_in_r