Gaussian primitives for deformable image registration

Deformable image registration (DIR) plays a critical role in radiotherapy by compensating for anatomical deformations. However, existing iterative and data-driven methods are often hindered by computational inefficiency or limited generalization. In response, our objective was to develop a novel optimization-based DIR method that reduces computational overhead and preserves the robust generalization of iterative methods while enhancing interpretability.

We proposed GaussianDIR, a novel DIR framework that explicitly represents the deformation field using a sparse set of adaptive Gaussian primitives. Each primitive is characterized by its centre, covariance, and associated local rigid deformation. Voxel-wise displacements are derived via blending the local rigid deformations of neighbouring primitives, enabling flexible yet efficient motion modelling.

On DIRLab lung dataset, GaussianDIR achieved a target registration error (TRE) of $1.00\pm 1.11$ millimeters in about 2.5 s, offering an effective trade-off between speed and precision for high-resolution images. On OASIS brain and ACDC cardiac datasets, the Dice similarity coefficient (DSC) improved from 80.6% to 81.3% and from 81.0% to 81.2% over previous state-of-the-art methods, respectively. Moreover, we compared the generalization performance of GaussianDIR and a data-driven method on IXI dataset, and found that GaussianDIR outperformed the data-driven method by 6.3% in DSC.

GaussianDIR combines high registration accuracy with computational efficiency, interpretability, and strong generalization performance. It challenged the conventional notion that iterative methods were inherently slow and overcomed the generalization limitations of data-driven methods, with potential for real-time clinical applications in radiotherapy.