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This paper presents a novel predictive model, MetaMorph, for metamorphic registration of images with appearance changes (i.e., caused by brain tumors). In contrast to previous learning-based registration methods that have little or no control over appearance-changes, our model introduces a new regularization that can effectively suppress the negative effects of appearance changing areas. In particular, we develop a piecewise regularization on the tangent space of diffeomorphic transformations (also known as initial velocity fields) via learned segmentation maps of abnormal regions. The geometric transformation and appearance changes are treated as joint tasks that are mutually beneficial. Our model MetaMorph is more robust and accurate when searching for an optimal registration solution under the guidance of segmentation, which in turn improves the segmentation performance by providing appropriately augmented training labels. We validate MetaMorph on real 3D human brain tumor magnetic resonance imaging (MRI) scans. Experimental results show that our model outperforms the state-of-the-art learning-based registration models. The proposed MetaMorph has great potential in various image-guided clinical interventions, e.g., real-time image-guided navigation systems for tumor removal surgery.