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

arXiv: https://arxiv.org/abs/2503.02606 · HTML: https://mlsanity.com/paper/2503.02606/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 83 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 30 of 40)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [Embodied Hands: Modeling and Capturing Hands and Bodies Together](https://mlsanity.com/paper/2201.02610/) (2022)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Unsupervised Deep Learning for Structured Shape Matching](https://mlsanity.com/paper/1812.03794/) (2018)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [Continuous and Orientation-preserving Correspondences via Functional Maps](https://mlsanity.com/paper/1806.04455/) (2018)
- [Smooth Shells: Multi-Scale Shape Registration with Functional Maps](https://mlsanity.com/paper/1905.12512/) (2019)
- [Partial Functional Correspondence](https://mlsanity.com/paper/1506.05274/) (2015)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators](https://mlsanity.com/paper/2108.09432/) (2021)
- [Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization](https://mlsanity.com/paper/2210.02870/) (2022)
- [Isometric Multi-Shape Matching](https://mlsanity.com/paper/2012.02689/) (2020)
- [A probabilistic model for the numerical solution of initial value problems](https://mlsanity.com/paper/1610.05261/) (2016)
- [RigNet: Neural Rigging for Articulated Characters](https://mlsanity.com/paper/2005.00559/) (2020)
- [Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective](https://mlsanity.com/paper/1810.03440/) (2018)
- [Product Manifold Filter: Non-Rigid Shape Correspondence via Kernel Density Estimation in the Product Space](https://mlsanity.com/paper/1701.00669/) (2017)
- [ZoomOut: Spectral Upsampling for Efficient Shape Correspondence](https://mlsanity.com/paper/1904.07865/) (2019)
- [A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty](https://mlsanity.com/paper/2006.01031/) (2020)
- [Structured Regularization of Functional Map Computations](https://mlsanity.com/paper/2009.14624/) (2020)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [The varifold representation of non-oriented shapes for diffeomorphic registration](https://mlsanity.com/paper/1304.6108/) (2013)
- [Calibrated Adaptive Probabilistic ODE Solvers](https://mlsanity.com/paper/2012.08202/) (2020)
- [Bayesian ODE Solvers: The Maximum A Posteriori Estimate](https://mlsanity.com/paper/2004.00623/) (2020)
- [Stable Implementation of Probabilistic ODE Solvers](https://mlsanity.com/paper/2012.10106/) (2020)
- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)

## Built on by (most cited first, 1 of 1)

- [Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach](https://mlsanity.com/paper/2509.06862/) (2025)

## Abstract (arXiv)

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.