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.
形变图像配准（DIR）是放射治疗中的一个基本任务，现有方法通常难以有效平衡计算效率、配准精度和速度。我们引入了一种新的DIR方法，该方法采用参数化的3D高斯控制点，实现了更好的权衡。该方法为3D体积医学图像之间的空间变形场提供了一个明确且灵活的表示，生成了覆盖所有体积位置的位移向量场（DVF）。通过局部插值转换，相关邻近高斯的变换来导出单个体素的移动，采用线性混合蒙皮（LBS）技术。这种插值策略不仅简化了体素运动的确定，还充当了有效的正则化技术。我们的方法通过反向传播，包含了一个统一的优化过程，使得能够迭代学习3D高斯的参数及其变换。此外，在学习阶段，高斯的密度根据运动复杂度的不同进行自适应调整。我们在4D-CT肺DIR-Lab和心脏ACDC数据集上验证了我们的方法，与现有方法相比，DIR-Lab数据集的平均目标配准误差（TRE）为1.06毫米，处理时间大幅缩短到2.43秒，显示出在精度和效率上的显著进步。