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Deep unsupervised representation learning for brain pathology segmentation is of great interest for medical imaging, as it does not require extensive annotations for training and allows the detection of unseen pathologies. While recent approaches proposed to model the distribution of healthy brain Magnetic Resonance Imaging (MRI) using variational autoencoders, we propose to model the pixel distribution of the healthy brain by introducing a shape-prior based on the brain tissue distribution. To this end, we propose Shape-Prior variational Autoencoders (SPA) to disentangle the generative factors of brain MRI, namely cerebrospinal fluid (CSF), gray matter (GM), and white matter (WM). Our method obtains interpretable latent representations, providing pixel-wise tissue probability maps. We evaluated the proposed method on MRIs of 538 patients from six data-sets containing demyelinating lesions, small vessel disease, and tumors. Experimental results indicate that our method is capable of disentangling the generative brain MR factors and avoiding the reconstruction of anomalous regions, leading to better lesion detection performance.
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