Partial-to-full registration remains challenging due to varying overlap ratios, fluctuating point densities, and the presence of noise. While transformers have shown strong potential for point cloud processing, prior methods typically confine them to global context aggregation, overlooking fine-grained local geometry crucial for accurate correspondence. We propose \emph{GAPR-Net}, a learning-based point cloud registration framework with a coarse-to-fine architecture that combines convolution and transformer modules, in which local and global information is fused between the partial and full point clouds using a cross-attention mechanism. To achieve this, a transformation-invariant point-wise geometric feature representation is proposed, which can robustly capture relative geometric features for individual points with respect to their neighboring points. To evaluate the effectiveness of the proposed approach, experiments are conducted on four geometrically distinct bones, including the tibia, femur, pelvis, and thoracic cartilage. The overall registration recall reaches 94.2\%, the method results in a low RMSE of 1.992 mm and $R^2$ values of 0.908 and 0.974 for rotation and translation, respectively. The results demonstrate that the proposed method effectively addresses the partial-to-full point cloud registration problem. The proposed method enables highly accurate 3D point cloud registration using partial observation, providing a critical foundation for precise surgical navigation and robotic interventions in computer-assisted surgery. The code will be accessed after the double-blind review process.

翻译：部分到整体的配准因重叠率变化、点密度波动以及噪声存在而仍具挑战性。尽管Transformer在点云处理中展现出强大潜力，但以往方法通常将其局限于全局上下文聚合，忽略了对应点匹配中关键的细粒度局部几何信息。我们提出GAPR-Net——一种基于学习的点云配准框架，采用由粗到精的架构，融合卷积与Transformer模块，通过交叉注意力机制在部分点云与完整点云之间融合局部与全局信息。为此，我们提出一种变换不变的点级几何特征表示方法，该方法能鲁棒地捕捉每个点相对于其邻域点的几何特征。为评估所提方法的有效性，我们在四个几何结构不同的骨骼（包括胫骨、股骨、骨盆和胸廓软骨）上进行了实验。整体配准召回率达到94.2%，该方法实现了低均方根误差（1.992毫米），旋转和平移的R²值分别为0.908和0.974。结果表明，所提方法有效解决了部分到整体的点云配准问题。该方法利用部分观测实现高精度三维点云配准，为计算机辅助手术中的精确手术导航和机器人干预奠定了关键基础。代码将在双盲评审后公开。