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Difficult image segmentation problems, for instance left atrium MRI, can beaddressed by incorporating shape priors to find solutions that are consistentwith known objects. Nonetheless, a single multivariate Gaussian is not anadequate model in cases with significant nonlinear shape variation or where theprior distribution is multimodal. Nonparametric density estimation is moregeneral, but has a ravenous appetite for training samples and poses seriouschallenges in optimization, especially in high dimensional spaces. Here, wepropose a maximum-a-posteriori formulation that relies on a generative imagemodel by incorporating both local intensity and global shape priors. We usedeep autoencoders to capture the complex intensity distribution while avoidingthe careful selection of hand-crafted features. We formulate the shape prior asa mixture of Gaussians and learn the corresponding parameters in ahigh-dimensional shape space rather than pre-projecting onto a low-dimensionalsubspace. In segmentation, we treat the identity of the mixture component as alatent variable and marginalize it within a generalizedexpectation-maximization framework. We present a conditional maximization-basedscheme that alternates between a closed-form solution for component-specificshape parameters that provides a global update-based optimization strategy, andan intensity-based energy minimization that translates the global notion of anonlinear shape prior into a set of local penalties. We demonstrate ourapproach on the left atrial segmentation from gadolinium-enhanced MRI, which isuseful in quantifying the atrial geometry in patients with atrial fibrillation.

Mixture Modeling of Global Shape Priors and Autoencoding Local Intensity Priors for Left Atrium Segmentation