An open source multivariate framework for n-tissue segmentation with evaluation on public data

Abstract

We introduce Atropos, an ITK-based multivariate n-class open source segmentation algorithm distributed with ANTs ( http://www.picsl.upenn.edu/ANTs). The Bayesian formulation of the segmentation problem is solved using the Expectation Maximization (EM) algorithm with the modeling of the class intensities based on either parametric or non-parametric finite mixtures. Atropos is capable of incorporating spatial prior probability maps (sparse), prior label maps and/or Markov Random Field (MRF) modeling. Atropos has also been efficiently implemented to handle large quantities of possible labelings (in the experimental section, we use up to 69 classes) with a minimal memory footprint. This work describes the technical and implementation aspects of Atropos and evaluates its performance on two different ground-truth datasets. First, we use the BrainWeb dataset from Montreal Neurological Institute to evaluate three-tissue segmentation performance via (1) K-means segmentation without use of template data; (2) MRF segmentation with initialization by prior probability maps derived from a group template; (3) Prior-based segmentation with use of spatial prior probability maps derived from a group template. We also evaluate Atropos performance by using spatial priors to drive a 69-class EM segmentation problem derived from the Hammers atlas from University College London. These evaluation studies, combined with illustrative examples that exercise Atropos options, demonstrate both performance and wide applicability of this new platform-independent open source segmentation tool.

Fig. 1

An adult brain image slice is shown with its ICM code image corresponding to a 5 × 5 MRF neighborhood. To the right of the ICM code image, we focus on a single neighborhood with a center voxel associated with the ICM code label of ‘10’. Each center voxel in a specified neighborhood exhibits a unique ICM code label which does not appear elsewhere in its neighborhood. When performing the segmentation labeling update for ICM, we iterate through the set of ICM code labels and, for each code label, we iterate through the image and update only those voxels associated with the current code label

Fig. 2

Flowchart illustrating Atropos usage typically beginning with bias correction via N4. Initialization provides an estimate before the iterative optimization in which the likelihood models for each class are tabulated from the current estimate followed by a recalculation of the posterior probabilities associated with each class. The multiple options associated with the different algorithmic components are indicated by the colored rounded rectangles connected to their respective core Atropos processes via curved dashed lines

Fig. 3

BrainWeb single-subject results for each tissue. The results show that N4 bias correction, combined with Atropos, results in a minimal effect of bias, even at the 40% level. The optimal β for the MRF term appears to be between 0.1 and 0.2. The legend is in the same position in each graph, allowing a visual comparison of the results. As one may see, the N4-assisted overlap values are consistent across bias field/RF inhomogeneity

Fig. 4

We combine N4 and Atropos by simple sequential processing and apply to BrainWeb T1-weighted single-subject data with 40% RF bias and 3% noise. The β for the MRF term is, here, 0.2. Slice 71 of the input data is in a. The initial K-means (K = 3) segmentation is in panel b. We use the brain mask to guide N4 bias correction and produce the image in c. We repeat the K-means segmentation, but with the N4-corrected image as input and produce the segmentation in d. The average 3-tissue Dice overlap of result b is 0.906 while the average overlap for d is 0.954. Arrows highlight a region of large before-after segmentation discrepancy. In e we see the BrainWeb proton density image with no inhomogeneity and 3% noise. Its segmentation is in f with average 3-tissue Dice overlap of 0.895. In g we use both proton density data and T1 data as multiple modality input to Atropos. The segmentation of this two-modality input data, using a multivariate Gaussian model, produces average 3-tissue Dice overlap of 0.958, which exceeds the univariate solution. An arrow highlights one region where there is small, visually recognizable improvement in sulcal segmentation relative to the result from T1 data alone. A second area of improvement is the putamen segmentation. The ground truth segmentation is in h. The multivariate segmentation result, in combination with the low PD segmentation performance, suggests PD and T1 provide complementary information that may improve 3-tissue segmentation and serves to validate the multivariate Atropos implementation. In this case, the benefit is likely to derive from the fact that the PD image has no bias

Fig. 5

BrainWeb 20-subject results for each tissue as a function of MRF-β parameter where MRF-β is in {0, 0.05, 0.1, 0.15, 0.2} and increases left to right. The results show that the PriorProbabilityImages with w = 0.5 (far right) gives the best performance for all tissues

Fig. 6

The figure compares the Dice overlap results from Atropos versus the raw results from majority voting for each of 68 neuroanatomical regions and, in addition, the unlabeled portions of the brain from the Hammers evaluation dataset. We evaluated Atropos via N-fold cross-validation and employed PriorProbabilityImages for each class where probabilities are gained by averaging mapped subject labels. The color coding highlights those regions that have the highest (yellow) and lowest (pink) improvement. The significance of the improvement, measured by pairwise T-test, is also shown as is a trinary coding of that improvement as: + significant improvement, – performance reduction, ~ no change

Listing 1

Atropos short command line menu which is invoked using the ‘-h’ option. The expanded menu, which provides details regarding the possible parameters and usage options, is elicited using the ‘--help option

Listing 2

N4 short command line menu which is invoked using the ‘-h’ option. The expanded menu, which provides details regarding the possible parameters and usage options, is elicited using the ‘--help’ option