Dear John & VBM people,
Here is an update about bias correction, in case anyone is interested. I was concerned about what level of bias correction was appropriate, so I tested it empirically (on a small scale) with our data. We had scans from 3 adults on 2 scans -- scans done on the same day, but the subject just came out and went back in the scanner. One subject had a benign subarachnoid cyst displacing about a quarter of the cerebellum.
I tested various methods of bias correction, including:
Very light 40 mm FWHM
Very light 60 mm FWHM
Very light 80 mm FWHM
With N3 prior to segment, then extremely heavy 150mm FWHM within SPM
To test a bias correction method, I segmented images at both timepoints with that method and subtracted the images. The idea was that the method that produced the least differences between the images was the truest, since there was no actual difference in brain volume between the scans. I took the absolute value of the subtracted image and summed up all the values...
You may be pleased to hear that for our data also, the default SPM "very light 60mm FWHM" was almost always the "best" by this definition of "least differences when there are known to be none". This was even more true if a gray or white matter mask was applied to exclude edgy voxels. Importantly, in cases where other methods (N3, or very light 80mm FWHM) were better, they were only slightly better, while in cases where "very light 60mm FWHM" was better, it was sometimes MUCH better - especially in the case of the subject with cyst. The variance and coeff of variance between methods was always smaller for white matter than gray matter, and variance was greatest for the subject with cyst.
So, now I can sleep easily knowing that we didn't just use the default, we justified using the default. :) Though, it should be noted that N3 also has a bunch of parameters to be tweaked, and I only tested the defaults for N3. Results were often similar between N3 and the SPM default; that was also reassuring.
From: John Ashburner [mailto:[log in to unmask]]
Sent: Thursday, January 22, 2009 6:53 AM
To: Dana Perantie; [log in to unmask]
Subject: Re: [SPM] bias correction - what level?
> I am using DARTEL in SPM8b to do longitudinal analyses of T1 images. For
> the initial Segment, I am looking at the different options for bias
> correction ranging from "very light" (default) to "extremely heavy". I
> tested all 6 levels of bias correction on one image. I applied the bias
> correction parameters from *seg_sn.mat to an image of all ones, using
> cspm_bias_writecorrected.m. This way the bias field that is applied can be
> visualized. I have attached the results as viewed in Check Reg, with "very
> light" entered first and all of them in order progressing up to "extremely
> heavy". I have a few questions...
> 1) Is it a concern that the shape of the brain is discernable? Might this
> mean that intensity data related to brain is being mistaken for intensity
> variation due to field inhomogeneity?
This is possible. The model assumes that each tissue class has fairly uniform
intensities throughout, but this is not necessarily the case. For example,
subcortical GM tends to have intensities that are closer to WM, so bias
correction may try to bring such GM to a similar intensity to that in the
cortex. If a region is darker for some physiological reason, then the bias
correction may attempt to "correct" this.
> 3) In some locations the intensity is adjusted down using the "very light"
> setting and up using the "extremely heavy" setting. The results appear to
> be qualitatively different; how can one decide which is best? Is there a
> recommendation what level of bias correction to use for longitudinal data,
> where we are especially concerned with potential influence of field change
> over time?
With little or no regularisation, the bias correction introduces ringing
effects ( http://en.wikipedia.org/wiki/Gibbs_phenomenon ) - particularly in
those regions of the image that are not modelled by the tissue classification
(ie far from the brain, where no tissue probability map information is
available). Ideally, the amount of regularisation should depend on prior
knowledge about the magnitude of the inhomogeneity artifact. Alternatively
(in principle), it could be determined using a type-II maximum likelihood
(REML) procedure - but in practice, the segmentation model would probably
need to be quite a lot more complicated for this to work well (eg proper MRF
modelling, multiple tissue class images for different kinds of GM, etc).
I tried to choose default settings that work as well as possible for typical
data. It is possible that some adjustments may be needed in order to tune
them. This would need to be done empirically, using cross-validation to
determine the most accurate segmentation.