C-NODDI: a constrained NODDI model for axonal density and orientation determinations in cerebral white matter

FSL (the FMRIB Software Library) is a comprehensive library of analysis tools for functional, structural and diffusion MRI brain imaging data, written mainly by members of the Analysis Group, FMRIB, Oxford. For this NeuroImage special issue on "20 years of fMRI" we have been asked to write about the history, developments and current status of FSL. We also include some descriptions of parts of FSL that are not well covered in the existing literature. We hope that some of this content might be of interest to users of FSL, and also maybe to new research groups considering creating, releasing and supporting new software packages for brain image analysis. Copyright © 2011 Elsevier Inc. All rights reserved.

The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogram-based model, the FM has an intrinsic limitation--no spatial information is taken into account. This causes the FM model to work only on well-defined images with low levels of noise; unfortunately, this is often not the the case due to artifacts such as partial volume effect and bias field distortion. Under these conditions, FM model-based methods produce unreliable results. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a MRF whose state sequence cannot be observed directly but which can be indirectly estimated through observations. Mathematically, it can be shown that the FM model is a degenerate version of the HMRF model. The advantage of the HMRF model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites. Although MRF modeling has been employed in MR image segmentation by other researchers, most reported methods are limited to using MRF as a general prior in an FM model-based approach. To fit the HMRF model, an EM algorithm is used. We show that by incorporating both the HMRF model and the EM algorithm into a HMRF-EM framework, an accurate and robust segmentation can be achieved. More importantly, the HMRF-EM framework can easily be combined with other techniques. As an example, we show how the bias field correction algorithm of Guillemaud and Brady (1997) can be incorporated into this framework to achieve a three-dimensional fully automated approach for brain MR image segmentation.