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

2025-03-04

AI Summary

This work addresses unsupervised physical interpolation and dense correspondence estimation between deformable 3D shapes (e.g., articulated human bodies). We propose a smooth, time-varying diffeomorphic flow field modeling framework based on Neural Ordinary Differential Equations (Neural ODEs). To our knowledge, this is the first method to jointly integrate varifold-based geometric metrics with skeleton-guided physical constraints—without requiring target pose priors or skinning weights—thereby effectively mitigating symmetry ambiguities while enforcing volume preservation and non-intersecting trajectories. The approach enables resolution-agnostic surface matching and handles high-fidelity models with inconsistent parameterizations. Evaluated on standard benchmarks, our method achieves state-of-the-art or superior performance in both interpolation quality and correspondence accuracy, significantly improving deformation robustness and physical plausibility.

Technology Category

Computer Vision: Diffusion Models for VisionMachine Learning: Learning with ManifoldsConstraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendationSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Unsupervised prediction of 3D shape interpolations.
• Automatic estimation of dense shape correspondence.
• Ensuring topological consistency and non-intersecting trajectories.

Innovation

• Neural ODEs model diffeomorphic 3D shape interpolation.
• Varifold formulation for efficient dense correspondence recovery.
• Skeleton-based constraints resolve deformation ambiguities without skinning.