Cardiac Magnetic Resonance (CMR) imaging is widely used for heart model reconstruction and digital twin computational analysis because of its ability to visualize soft tissues and capture dynamic functions. However, CMR images have an anisotropic nature, characterized by large inter-slice distances and misalignments from cardiac motion. These limitations result in data loss and measurement inaccuracies, hindering the capture of detailed anatomical structures. In this work, we introduce MorphiNet, a novel network that reproduces heart anatomy learned from high-resolution Computed Tomography (CT) images, unpaired with CMR images. MorphiNet encodes the anatomical structure as gradient fields, deforming template meshes into patient-specific geometries. A multilayer graph subdivision network refines these geometries while maintaining a dense point correspondence, suitable for computational analysis. MorphiNet achieved state-of-the-art bi-ventricular myocardium reconstruction on CMR patients with tetralogy of Fallot with 0.3 higher Dice score and 2.6 lower Hausdorff distance compared to the best existing template-based methods. While matching the anatomical fidelity of comparable neural implicit function methods, MorphiNet delivered 50 $\times$ faster inference. Cross-dataset validation on the Automated Cardiac Diagnosis Challenge confirmed robust generalization, achieving a 0.7 Dice score with 30\% improvement over previous template-based approaches. We validate our anatomical learning approach through the successful restoration of missing cardiac structures and demonstrate significant improvement over standard Loop subdivision. Motion tracking experiments further confirm MorphiNet's capability for cardiac function analysis, including accurate ejection fraction calculation that correctly identifies myocardial dysfunction in tetralogy of Fallot patients.

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