ContiMorph: An unsupervised learning framework for cardiac motion tracking with time-continuous diffeomorphism

Cardiac motion tracking is essential for evaluating cardiac function and diagnosing cardiovascular diseases. However, existing tracking methods primarily depend on scaling-and-squaring (SS) integration to derive discrete Lagrangian motion fields. This dependency limits the ability to fully exploit the temporal continuity of cardiac motion, leading to suboptimal tracking accuracy. In this paper, we introduce ContiMorph, a novel unsupervised learning framework for time-continuous motion tracking in cardiac image sequences. Specifically, ContiMorph integrates a frame-aware U-Net with time-embedded transformer module to learn temporally continuous intra-frame motion fields, which are then composed into time-continuous Lagrangian motion fields for precise tracking. Moreover, we propose a time-continuous Lagrangian motion constraint to ensure diffeomorphic topology throughout the image sequence. Combined with semigroup regularization during training, this constraint effectively leverages temporal information and eliminates the need for SS integration. Extensive experiments on cardiac magnetic resonance imaging (MRI) and echocardiography (US) datasets demonstrate that ContiMorph outperforms existing motion-tracking methods, achieving state-of-the-art performance across diverse imaging modalities. The code is publicly available at https://github.com/luffhhh/ContiMorph.