Unsupervised domain adaptation approaches have recently succeeded in various medical image segmentation tasks. The reported works often tackle the domain shift problem by aligning the domain-invariant features and minimizing the domain-specific discrepancies. That strategy works well when the difference between a specific domain and between different domains is slight. However, the generalization ability of these models on diverse imaging modalities remains a significant challenge. This paper introduces UDA-VAE++, an unsupervised domain adaptation framework for cardiac segmentation. We show that the evidence lower bound of VAE-based domain adaptation penalizes the mutual information between the image and the latent space, including the structure information that segmentation relies on. Maximizing the structure mutual information removes this penalty on the structure information, while the remaining information is still compressed. To estimate this term, we develop a novel Structure Mutual Information Estimation (SMIE) block with a global estimator, a local estimator, and a prior information matching estimator to maximize the mutual information between the reconstruction and segmentation tasks. Specifically, we design a novel sequential reparameterization scheme that enables information flow and variance correction from the low-resolution latent space to the high-resolution latent space. Comprehensive experiments on benchmark cardiac segmentation datasets demonstrate that our model outperforms previous state-of-the-art qualitatively and quantitatively. The code is available at https://github.com/LOUEY233/Toward-Mutual-Information

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