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An Open Source Multivariate Framework for n-Tissue Segmentation with Evaluation on Public Data

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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.

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Notes

  1. Atropos is one of the three Fates from Greek mythology characterized by her dreaded shears used to decide the destiny of each mortal. Also, consistent with the entomological motif of our ANTs, Acherontia atropos is a species of large moth known for the skull-like pattern visible on its thorax.

  2. In the classic 3-tissue segmentation case, each voxel in the brain region is assigned a label of ‘cerebrospinal fluid (csf)’, ‘gray matter (gm)’, or ‘white matter (wm)’.

  3. Using a more expansive definition of U(x),

    $$ U(\mathbf{x}) = \sum\limits_{i = 1}^N \left( V_i(x_i) + \beta \sum\limits_{j \in \mathcal{N}_i} V_{ij}( x_i, x_j ) \right) $$

    would permit casting the other prior terms inside the definition of U(x) in the form of the external field V i (x i ) but, for clarity purposes, we consider them separately.

  4. Due to the lack of parameters in the non-parametric approach, it is not technically an EM algorithm (as described in Wells et al. (1996)). However, the same iterative maximization is applicable and is quite robust in practice as evidenced by the number of researchers employing non-parametric models (see the Introduction).

  5. Consider N sites each with a possible K labels for a total of N K possible labeling configurations. For large K ≫ 3, exact optimization is even more intractable than for the traditional 3-tissue scenario.

  6. http://www.itk.org/Doxygen/html/classitk_1_1N4MRIBiasFieldCorrectionImageFilter.html

  7. A comprehensive evaluation of N4 reported in Tustison et al. (2010a) used the BrainWeb data set to compare performance with the original N3 algorithm (Sled et al. 1998).

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Acknowledgement

This work was supported in part by NIH (AG17586, AG15116, NS44266, and NS53488).

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Authors and Affiliations

  1. Penn Image Computing and Science Laboratory, University of Pennsylvania, 3600 Market Street, Suite 370, Philadelphia, PA, 19104, USA

    Brian B. Avants, Jue Wu, Philip A. Cook & James C. Gee

  2. Department of Radiology and Medical Imaging, University of Virginia, Charlottesville, VA, USA

    Nicholas J. Tustison

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  1. Brian B. Avants
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Avants, B.B., Tustison, N.J., Wu, J. et al. An Open Source Multivariate Framework for n-Tissue Segmentation with Evaluation on Public Data. Neuroinform 9, 381–400 (2011). https://doi.org/10.1007/s12021-011-9109-y

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