Topology-Preserving Implicit Template Learning via Bidirectional Deformation for 3D Shape Reconstruction and Registration

Deep Implicit Functions (DIFs) represent 3D objects continuously using parameterized deep neural networks but struggle with establishing point correspondences across shapes. To address this, recent approaches combine deformation and template fields to learn implicit templates. However, these methods often neglect the adjacency relationships among points, leading to suboptimal results. To overcome this, we propose a novel framework that introduces an inverse deformation step during training to enhance the topology preservation of deformation fields. By establishing dense point correspondences between shape instances and templates through bidirectional deformation, our method ensures that corresponding points maintain proximity on their respective surfaces. Experimental results on multiple datasets demonstrate that our approach outperforms state-of-theart methods in shape representation and registration tasks, with a significant improvement in normal consistency, highlighting the importance of the proposed inverse deformation process for achieving accurate correspondences.