让形状重构模型能处理撕裂、切割等拓扑变化，突破传统方法局限。
Generalizing Shape-from-Template to Topological Changes
- 通过分区调整模板空间，迭代优化能量函数实现拓扑变化下的重建
- 在合成与真实数据上均优于基线方法，可稳定处理撕裂和切割
- 适合需要处理复杂形变的3D重建任务，如医疗影像或柔性物体建模
从3D模板与2D图像之间的对应关系重建可变形物体表面是形态恢复模板（Shape-from-Template, SfT）研究的核心问题；然而，当形变伴随拓扑变化时，现有方法失效。本文提出一种原则性扩展的SfT框架，可在拓扑变化下实现稳定重建。方法以经典SfT解为初始，通过划分模板空间域，迭代优化一个联合编码物理合理性与重投影一致性的能量函数。实验表明，该方法能鲁棒地捕捉多种实际相关的拓扑事件，如二维有界表面上的撕裂与切割，首次建立了具备拓扑变化感知能力的SfT通用框架。在合成与真实数据上的测试均显示，本方法持续优于基线方法。
原文摘要 · Abstract (English)
Reconstructing the surfaces of deformable objects from correspondences between a 3D template and a 2D image is well studied under Shape-from-Template (SfT) methods; however, existing approaches break down when topological changes accompany the deformation. We propose a principled extension of SfT that enables reconstruction in the presence of such changes. Our approach is initialized with a classical SfT solution and iteratively adapts the template by partitioning its spatial domain so as to minimize an energy functional that jointly encodes physical plausibility and reprojection consistency. We demonstrate that the method robustly captures a wide range of practically relevant topological events including tears and cuts on bounded 2D surfaces, thereby establishing the first general framework for topological-change-aware SfT. Experiments on both synthetic and real data confirm that our approach consistently outperforms baseline methods.
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