A key concept in medical image analysis is the idea of a mean template, i.e., a statistical average around which deviations can be assessed. In the context of white matter fiber analysis, we seek to represent an anatomically defined fiber bundle with a mean and variance that describes its essential characteristics. This mean is of interest for practical reasons that go beyond atlas construction. From my hard-won experience working with DTI fibers, these are 3 reasons we need to compute means:
1.There are a large number of fibers involved in white matter fiber analysis. The corpus callosum has over 300 million fibers alone, the whole brain, 100 billion! fibers--source: Mori's atlas. The tractography output which is some fraction of this can still be several thousand fibers. Due to this large volume, a practical first step in any study, and one that is advocated by me, is to compute a representative mean of a fiber bundle.
2. The tractography output is subject to error. Noise, imperfections in the image and the presence of regions of low anisotropy due to fiber crossings all contribute to this.
In order to make the streamline output more robust we can average over the fiber bundle. This strategy is also useful when a representative bundle is sought and there are discontinuities and other fiber damage due to disease.
3. To facilitate statistical analysis for population studies where the underlying problem is one of assigning membership to a group.
Means may be computed for the following situations:
i)for a group of fibers within a fiber bundle
ii) for an intra- or inter-subject collection of fibers from many bundles
iii)for an intra- or inter-subject collection of means of fiber bundles
The computation of statistical summaries is usually part of any framework for white matter
fiber analysis. Some of these frameworks are listed in my previous post on Mathematical frameworks.