解决拓扑错误下的非刚性3D网格匹配问题，无需数据驱动先验。
Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach
- 提出自适应拓扑的形变模型，支持拓扑变化以匹配形状对
- 联合优化模板网格与对齐结果，在有拓扑瑕疵时仍保持高精度
- 适用于噪声多视图重建，性能超越大量数据训练的方法
非刚性3D网格匹配是计算机视觉与图形学中的关键步骤。现有方法常假设真实对应关系诱导的形变为近等距或ARAP型，但这些假设在输入形状存在拓扑伪影时失效。我们针对真实场景如逐帧多视角重建中常见的拓扑问题，提出一种拓扑自适应形变模型，允许形状拓扑变化，同时满足ARAP和双射对应约束。基于该模型，我们联合优化一个具有合理拓扑的模板网格及其与待匹配形状的对齐，从而提取对应关系。实验表明，本方法不依赖任何数据驱动先验，仍可处理高度非等距及含拓扑伪影的形状，包括噪声多视图重建结果，其3D对齐质量甚至优于在大规模数据上训练的方法。
原文摘要 · Abstract (English)
Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps assume the deformation induced by the ground truth correspondences to be near-isometric, ARAP-like deformation-guided approaches assume the latter to be ARAP. Neither assumption holds in certain topological configurations of the input shapes. We are motivated by real-world scenarios such as per-frame multi-view reconstructions, often suffering from topological artefacts. To this end, we propose a topology-adaptive deformation model allowing changes in shape topology to align shape pairs under ARAP and bijective association constraints. Using this model, we jointly optimise for a template mesh with adequate topology and for its alignment with the shapes to be matched to extract correspondences. We show that, while not relying on any data-driven prior, our approach applies to highly non-isometric shapes and shapes with topological artefacts, including noisy per-frame multi-view reconstructions, even outperforming methods trained on large datasets in 3D alignment quality.
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