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Abstract

Non-rigid point cloud registration is a crucial task for aligning 3D data when objects undergo deformation due to motion, pressure, or biological processes. This is especially important in high-stakes domains such as surgical navigation, where anatomical structures often bend, compress, or stretch in unpredictable ways. Despite recent progress, current methods continue to struggle with large deformations, noisy or partial observations, and generalization to real-world scenarios. Moreover, many approaches fail to integrate both local and global spatial learning or to account for uncertainty in ambiguous regions.

This thesis introduces a multi-stage framework for non-rigid point cloud registration, comprising three progressively refined learning models. First, Robust-DefReg encodes local geometric structures using graph convolutions to build deformation-aware descriptors. Next, DefTransNet incorporates global learning through a hybrid Transformer–Graph architecture that explicitly resolves feature ambiguity via cross-attention between source and target point clouds. Finally, Learning-to-Refine introduces a probabilistic iterative refinement strategy that regularizes deformation prediction using KL divergence over learned feature distributions, addressing uncertainty in ambiguous and partially observed regions. Together, these models directly respond to the core research questions on local representation, global context, and uncertainty modeling posed in this dissertation.

To enable reproducible benchmarking across diverse deformation levels, two datasets were developed: SynBench, a synthetic dataset with controlled and progressively increasing deformation levels; and DeformedTissue, a real-world dataset based on simulated anatomical tissue deformation. Additionally, all methods were evaluated on two widely used public benchmarks, ModelNet40 and 4DMatch, to validate generalization across domains. Experimental results reveal a clear progression in performance across the proposed methods. DefTransNet outperforms state-of-the-art baselines by achieving high accuracy and stability under severe deformations, while Learning-to-Refine introduces probabilistic refinement that further improves convergence and consistency. Evaluation across synthetic, real-world, and public datasets confirms the generalizability of the framework. Notably, the deformation–robustness plots indicate that the performance of our proposed methods remains stable even under extreme deformation levels, suggesting that, within the scope of this study, the core challenge of deformation in non-rigid point cloud registration has been effectively addressed.