Deformable image registration (DIR) is a fundamental task in radiotherapy,
with existing methods often struggling to balance computational efficiency,
registration accuracy, and speed effectively. We introduce a novel DIR approach
employing parametric 3D Gaussian control points achieving a better tradeoff. It
provides an explicit and flexible representation for spatial deformation fields
between 3D volumetric medical images, producing a displacement vector field
(DVF) across all volumetric positions. The movement of individual voxels is
derived using linear blend skinning (LBS) through localized interpolation of
transformations associated with neighboring Gaussians. This interpolation
strategy not only simplifies the determination of voxel motions but also acts
as an effective regularization technique. Our approach incorporates a unified
optimization process through backpropagation, enabling iterative learning of
both the parameters of the 3D Gaussians and their transformations.
Additionally, the density of Gaussians is adjusted adaptively during the
learning phase to accommodate varying degrees of motion complexity. We
validated our approach on the 4D-CT lung DIR-Lab and cardiac ACDC datasets,
achieving an average target registration error (TRE) of 1.06 mm within a
much-improved processing time of 2.43 seconds for the DIR-Lab dataset over
existing methods, demonstrating significant advancements in both accuracy and
efficiency.

采用参数化的三维高斯控制点的变形图像配准方法，在计算效率、配准精度和速度之间取得了更好的平衡，通过局部插值转换，实现了对三维体积医学图像之间的空间变形场进行明确灵活的表示，进而在后向传播的统一优化过程中迭代学习了三维高斯和其变换的参数，取得了在精度和效率方面的显著进展。