Abstract
Difficult image segmentation problems, e.g., left atrium in MRI, can be addressed by incorporating shape priors to find solutions that are consistent with known objects. Nonetheless, a single multivariate Gaussian is not an adequate model in cases with significant nonlinear shape variation or where the prior distribution is multimodal. Nonparametric density estimation is more general, but has a ravenous appetite for training samples and poses serious challenges in optimization, especially in high dimensional spaces. Here, we propose a maximum-a-posteriori formulation that relies on a generative image model by incorporating both local intensity and global shape priors. We use deep autoencoders to capture the complex intensity distribution while avoiding the careful selection of hand-crafted features. We formulate the shape prior as a mixture of Gaussians and learn the corresponding parameters in a high-dimensional shape space rather than pre-projecting onto a low-dimensional subspace. In segmentation, we treat the identity of the mixture component as a latent variable and marginalize it within a generalized expectation-maximization framework. We present a conditional maximization-based scheme that alternates between a closed-form solution for component-specific shape parameters that provides a global update-based optimization strategy, and an intensity-based energy minimization that translates the global notion of a nonlinear shape prior into a set of local penalties. We demonstrate our approach on the left atrial segmentation from gadolinium-enhanced MRI, which is useful in quantifying the atrial geometry in patients with atrial fibrillation.
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- 1.
For notational simplicity, we will refer to \(p(\mathcal {Z}= z) = p(\mathcal {Z})\) hereafter.
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Acknowledgment
This work was supported by the National Institutes of Health [grant numbers R01-HL135568-01 and P41-GM103545-19].
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Sodergren, T., Bhalodia, R., Whitaker, R., Cates, J., Marrouche, N., Elhabian, S. (2019). Mixture Modeling of Global Shape Priors and Autoencoding Local Intensity Priors for Left Atrium Segmentation. In: Pop, M., et al. Statistical Atlases and Computational Models of the Heart. Atrial Segmentation and LV Quantification Challenges. STACOM 2018. Lecture Notes in Computer Science(), vol 11395. Springer, Cham. https://doi.org/10.1007/978-3-030-12029-0_39
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DOI: https://doi.org/10.1007/978-3-030-12029-0_39
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