Purpose: Accurate point cloud registration is essential in computer-aided interventions (CAI) to align multi-modal medical images for intraoperative guidance. Classical methods, such as Iterative Closest Point (ICP), remain attractive for their explainability and minimal training requirements, but typically ignore anatomical semantics and biomechanical properties during regularization. Methods: We present Semantic ICP (SemICP), a novel non-rigid point cloud registration framework that combines semantically informed point matching with deformation regularization. Semantic labels are used to improve correspondence matching by constraining correspondences to be anatomically consistent. A novel control-point deformation representation with linear-elastic energy regularization is introduced to encourage biomechanically plausible deformations. SemICP was evaluated on four datasets on US-CT, MR-CT, MR-MR and MR-US registration against established baselines. It was also tested with labels from AI-based segmentation in a fully automatic segmentation-registration pipeline. Results: Across all datasets, SemICP achieves lower Hausdorff distance, mean surface distance, and target registration error than competing methods. The fully automatic registration pipeline was shown to be effective for US-MR registration and to improve the alignment of expert-annotated structures. Conclusion: SemICP improves deformable point cloud registration accuracy and robustness by combining semantic correspondence constraints and linear energy regularization. Combined with AI-based segmentation, SemICP provides an effective pipeline for multi-modal registration in CAI.

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