用流模型实现3D形状间高效映射，无需训练即可跨模态匹配。
FUSE: A Flow-based Mapping Between Shapes
- 基于可逆流模型构建形状映射，通过锚点分布统一表示不同数据格式。
- 在多种基准上实现高覆盖率和精度，支持点云、网格、SDF等跨模态匹配。
- 适用于形状匹配、UV映射、人体点云注册等任务，通用性强。
我们提出一种基于流匹配模型的新型神经表示方法，用于3D形状间的映射。3D形状被表示为从固定锚点分布出发的连续可逆流映射所诱导的概率分布。给定源形状和目标形状，通过组合反向流（源到锚点）与正向流（锚点到目标），实现两表面之间的点映射。通过点级任务定制嵌入编码形状，该方法提供了一种可逆且模态无关的形状间映射表示，适用于点云、网格、符号距离场（SDF）和体素数据。结果在多样化的基准测试和挑战性场景中表现出一致的高覆盖度与高精度。除形状匹配外，本框架在UV映射及人体原始点云扫描配准等任务中也展现出良好性能。
原文摘要 · Abstract (English)
We introduce a novel neural representation for maps between 3D shapes based on flow-matching models, which is computationally efficient and supports cross-representation shape matching without large-scale training or data-driven procedures. 3D shapes are represented as the probability distribution induced by a continuous and invertible flow mapping from a fixed anchor distribution. Given a source and a target shape, the composition of the inverse flow (source to anchor) with the forward flow (anchor to target), we map points between the two surfaces. By encoding the shapes with a pointwise task-tailored embedding, this construction provides an invertible and modality-agnostic representation of maps between shapes across point clouds, meshes, signed distance fields (SDFs), and volumetric data. The resulting representation consistently achieves high coverage and accuracy across diverse benchmarks and challenging settings in shape matching. Beyond shape matching, our framework shows promising results in other tasks, including UV mapping and registration of raw point cloud scans of human bodies.
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