Registering intraoperative Ultrasound (US) bone-surface point clouds to preoperative Computed Tomography (CT) models can support radiation-free orthopedic navigation. Differences in imaging physics produce distinct surface sampling patterns, complicating cross-modal feature matching. Bone strongly reflects ultrasound and casts an acoustic shadow, so US captures only the probe-facing bone surface and leaves most CT points unmatched. This partial coverage makes correspondences ambiguous on near-symmetric bones. We propose CUFormer, a modality-aware registration framework. We introduce a Modality-Aware Transformer (MAT) that encodes input modality through identity embeddings and updates features through modality-specific adapters within a shared geometric matcher. We model imaging visibility and use predicted reference-side visibility to weight coarse and fine correspondences. CUFormer achieves the lowest mean registration errors among evaluated methods on two CT-US datasets, UltraBones100k and UltraBonesHip, and the CT-RGB-D dataset SpineDepth. On UltraBones100k, it reaches mean rotation error 4.53$^\circ$, translation error 3.19\,mm, and Root Mean Squared Error (RMSE) 2.54\,mm, reducing RMSE by 65.8\% relative to the best-performing baseline by this metric. These results demonstrate CUFormer's effectiveness in aligning partial bone surfaces with preoperative CT across anatomical sites.

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