  Deformable image registration (DIR) is crucial in medical image analysis,
enabling the exploration of biological dynamics such as organ motions and
longitudinal changes in imaging. Leveraging Neural Ordinary Differential
Equations (ODE) for registration, this extension work discusses how this
framework can aid in the characterization of sequential biological processes.
Utilizing the Neural ODE's ability to model state derivatives with neural
networks, our Neural Ordinary Differential Equation Optimization-based (NODEO)
framework considers voxels as particles within a dynamic system, defining
deformation fields through the integration of neural differential equations.
This method learns dynamics directly from data, bypassing the need for physical
priors, making it exceptionally suitable for medical scenarios where such
priors are unavailable or inapplicable. Consequently, the framework can discern
underlying dynamics and use sequence data to regularize the transformation
trajectory. We evaluated our framework on two clinical datasets: one for
cardiac motion tracking and another for longitudinal brain MRI analysis.
Demonstrating its efficacy in both 2D and 3D imaging scenarios, our framework
offers flexibility and model agnosticism, capable of managing image sequences
and facilitating label propagation throughout these sequences. This study
provides a comprehensive understanding of how the Neural ODE-based framework
uniquely benefits the image registration challenge.
