无需对应点即可实现3D物体自然变形与匹配，支持复杂物理约束。
ARC-Flow : Articulated, Resolution-Agnostic, Correspondence-Free Matching and Interpolation of 3D Shapes Under Flow Fields
- 用神经微分方程构建流动场，实现拓扑一致的连续形变。
- 在标准数据集上对应与插值效果优于现有方法，精度更高。
- 仅需源形体骨架即可建模，适合无预知目标姿态的场景。
本文提出一种统一框架，用于无监督预测两个3D可动形状之间的物理合理插值，并自动估算它们之间的密集对应关系。插值通过由神经常微分方程（Neural ODEs）控制的平滑时变流场建模，确保拓扑一致性与轨迹不相交，同时兼容硬约束（如体积守恒）和软约束（如物理先验）。对应关系通过高效的变流形（Varifold）公式恢复，适用于参数化不同的高保真表面。仅需提供源形状的简单骨骼结构，即可对变形场施加物理驱动约束并解决对称性歧义，且无需皮肤权重或目标姿态先验知识。定性和定量结果表明，在标准数据集上，该方法在形状对应与插值任务中的表现达到或超越现有最先进水平。
原文摘要 · Abstract (English)
This work presents a unified framework for the unsupervised prediction of physically plausible interpolations between two 3D articulated shapes and the automatic estimation of dense correspondence between them. Interpolation is modelled as a diffeomorphic transformation using a smooth, time-varying flow field governed by Neural Ordinary Differential Equations (ODEs). This ensures topological consistency and non-intersecting trajectories while accommodating hard constraints, such as volume preservation, and soft constraints, \eg physical priors. Correspondence is recovered using an efficient Varifold formulation, that is effective on high-fidelity surfaces with differing parameterisations. By providing a simple skeleton for the source shape only, we impose physically motivated constraints on the deformation field and resolve symmetric ambiguities. This is achieved without relying on skinning weights or any prior knowledge of the skeleton's target pose configuration. Qualitative and quantitative results demonstrate competitive or superior performance over existing state-of-the-art approaches in both shape correspondence and interpolation tasks across standard datasets.
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