ARC-Flow : Articulated, Resolution-Agnostic, Correspondence-Free Matching and Interpolation of 3D Shapes Under Flow Fields

TL;DR

ARC-Flow presents an unsupervised framework for predicting physically plausible interpolations and automatic dense correspondences between two 3D articulated shapes. It models deformations as a time-varying, diffeomorphic flow governed by Neural ODEs with volume preservation, and it uses a Varifold-based metric to achieve correspondence-free matching. A skeleton-driven transformation coupled with soft tissue priors promotes local rigidity around bones while allowing tissue deformation, and a Varifold compression scheme enables efficient scaling to high-resolution meshes. Across DFAUST, MANO, and SMAL, ARC-Flow achieves competitive or superior performance on interpolation quality and correspondence accuracy, while maintaining topological integrity and offering automatic skeleton transfer. The work delivers a scalable, unsupervised pipeline for realistic shape morphing and rigging transfer in challenging real-world settings.

Abstract

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.

Figures (20)

• Figure 1: Top: 3D shape interpolation. Our method obtains a more reliable interpolation than existing state-of-the-art approaches (e.g. Spectral Meets Spatial cao2024spectral) even under substantial non-isometric deformation. Samples taken at $t = {0.25, 0.5, 0.75}$ and $1.0=:T$ along the deformation path. Bottom: Scaling to high-resolution meshes. Using Varifold compression we obtain dramatic computational savings, while maintaining similar perceptual quality, allowing us to scale to high resolution meshes.
• Figure 2: Left: Method overview. We transform the source shape to match the target using a diffeomorphic differential vector field; we also recover the forward kinematic transformation of the source skeleton. Matching is performed with a correspondence-free Varifold metric. Right: Varifold field. Visualisation of an implicit Varifold field for intuition; computation of $\vec{\mathbf{v}}(\mathbf{x})$ is not required for matching.
• Figure 3: Skeleton loss. We encourage the flow to match an estimated rigid transform for points within the cylindrical "bones".
• Figure 4: Soft tissue loss. We penalise arbitrary deformation of the soft tissue (and surface) using physically inspired priors to minimise shear/strain energy throughout the flow.
• Figure 5: Interpolation results for DFAUST vs SMS cao2024spectral. Mean and confidence intervals for the three metrics are shown; top row has our results and bottom show SMS. Our method improves across all metrics and also has narrower error bars indicating more consistent performance. Please zoom for details.