A Bayesian model of shape and appearance for subcortical brain segmentation

Abstract

Automatic segmentation of subcortical structures in human brain MR images is an important but difficult task due to poor and variable intensity contrast. Clear, well-defined intensity features are absent in many places along typical structure boundaries and so extra information is required to achieve successful segmentation. A method is proposed here that uses manually labelled image data to provide anatomical training information. It utilises the principles of the Active Shape and Appearance Models but places them within a Bayesian framework, allowing probabilistic relationships between shape and intensity to be fully exploited. The model is trained for 15 different subcortical structures using 336 manually-labelled T1-weighted MR images. Using the Bayesian approach, conditional probabilities can be calculated easily and efficiently, avoiding technical problems of ill-conditioned covariance matrices, even with weak priors, and eliminating the need for fitting extra empirical scaling parameters, as is required in standard Active Appearance Models. Furthermore, differences in boundary vertex locations provide a direct, purely local measure of geometric change in structure between groups that, unlike voxel-based morphometry, is not dependent on tissue classification methods or arbitrary smoothing. In this paper the fully-automated segmentation method is presented and assessed both quantitatively, using Leave-One-Out testing on the 336 training images, and qualitatively, using an independent clinical dataset involving Alzheimer's disease. Median Dice overlaps between 0.7 and 0.9 are obtained with this method, which is comparable or better than other automated methods. An implementation of this method, called FIRST, is currently distributed with the freely-available FSL package.

Fig. 1

A coronal slice from a single subject’s images in the training set. a) MR T₁-weighted image. b) Manual segmentation overlaying the T₁-weighted image.

Fig. 2

Illustration of the directions of the applied displacements: s_n is the normal vector; s_t is the surface tangent vector; and s_Amax is the bisector of the largest neighbouring triangle.

Fig. 3

First mode of variation for the left thalamus. The first column shows the thalamus surface overlaid on the MNI152 template. The second column is a zoomed view, with the conditional mean intensity shown near the thalamus border, within the square patch. A lower position for the thalamus corresponds to an enlarged ventricle which correlates with the darker band of intensities at the thalamus border (due to more surrounding CSF). See text for a fuller explanation.

Fig. 4

Example of a subcortical segmentation from the LOO tests, as described in the text.

Fig. 5

Boxplots of the Dice overlap between the filled surfaces and the manual labels for each of the 15 structures. All structures were segmented using the number of modes of variation and both prior constants ε_i and ε_s, as specified in Table 2. The prior constants are defined as a percentage of the total variance in the training set. The FAST-based method was used for boundary correction, with the exception of the thalamus and pallidum where all voxels were included (see text).

Fig. 6

The mean Dice overlap between the filled surfaces and the manual labels for each of the 15 structures when restricting the fitting to 20, 30, 40, 50, 60, 70, 80, 90 and 100 modes of variation (in different colours — see key on the right hand side). All structures used the FAST method for boundary correction and had both prior constants ε_i and ε_s as specified in Table 2.

Fig. 7

Effect of ε_s and ε_I on Dice overlap using LOO cross-validation.

Fig. 8

Vertex analysis results for the AD dataset: shows the right hippocampus, amygdala and thalamus. In (a) the results are colour-coded by uncorrected F-statistic values, while in (b) the colour-coding corresponds to the corrected p-values using FDR. In (a) the vectors represent the mean difference between the groups (AD and controls).