Three validation metrics for automated probabilistic image segmentation of brain tumours

Abstract

The validity of brain tumour segmentation is an important issue in image processing because it has a direct impact on surgical planning. We examined the segmentation accuracy based on three two-sample validation metrics against the estimated composite latent gold standard, which was derived from several experts' manual segmentations by an EM algorithm. The distribution functions of the tumour and control pixel data were parametrically assumed to be a mixture of two beta distributions with different shape parameters. We estimated the corresponding receiver operating characteristic curve, Dice similarity coefficient, and mutual information, over all possible decision thresholds. Based on each validation metric, an optimal threshold was then computed via maximization. We illustrated these methods on MR imaging data from nine brain tumour cases of three different tumour types, each consisting of a large number of pixels. The automated segmentation yielded satisfactory accuracy with varied optimal thresholds. The performances of these validation metrics were also investigated via Monte Carlo simulation. Extensions of incorporating spatial correlation structures using a Markov random field model were considered.

Figure 1

Beta distributions used in the simulation study for non-tumour (C₀) class only; the Beta distributions for the tumour (C₁) class may be graphed similarly and are omitted here.

Figure 2

The grey scale MR image of a case of a meningioma (Case 1).

Figure 3

Estimated composite pixel-wise gold standard of an MRI case of a meningioma (Case 1).

Figure 4

Estimated mixture of two beta distributions of an MRI case of a meningioma (Case 1).

Figure 5

Estimated ROC curves for the nine brain tumour cases by tumour type: meningiomas (left panel), astrocytomas (centre panel), and other low-grade gliomas (right panel).

Figure 6

Pixel-wise frequency of segmentation decision by three expert raters and the estimated pixel-wise gold standard by MRF modelling of a meningioma (Case 1): Left Panel: Frequency of selection; Right Panel: Estimated gold standard by an MRF model, which is virtually identical to that estimated by a pixel-wise independent model.