In summary, the innovative CPT-DIR approach, integrating principles of INR and LDDMM, represents a11 significant departure from traditional voxel-based methods in DIR. By adopting a paradigm of continuous motion modelling, we transcend the limitations inherent in voxel-based representations, offering a more robust, automatic and versatile solution. Leveraging spatial continuity, we effectively handle the intricacies of sliding organ boundaries, while temporal continuity alleviates the complexities associated with significant anatomical changes over time. The tangible benefits are evident in its superior performance compared to classic B-splines methods. CPT-DIR consistently achieves better performance by all kinds of evaluation matrices. Additionally, the efficiency gains are substantial, with registration times slashed by more than half.