  Regression on medical image sequences can capture temporal image pattern
changes and predict images at missing or future time points. However, existing
geodesic regression methods limit their regression performance by a strong
underlying assumption of linear dynamics, while diffusion-based methods have
high computational costs and lack constraints to preserve image topology. In
this paper, we propose an optimization-based new framework called NODER, which
leverages neural ordinary differential equations to capture complex underlying
dynamics and reduces its high computational cost of handling high-dimensional
image volumes by introducing the latent space. We compare our NODER with two
recent regression methods, and the experimental results on ADNI and ACDC
datasets demonstrate that our method achieves the state-of-the-art performance
in 3D image regression. Our model needs only a couple of images in a sequence
for prediction, which is practical, especially for clinical situations where
extremely limited image time series are available for analysis. Our source code
is available at https://github.com/ZedKing12138/NODER-pytorch.
