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

Adam Hartshorne, Allen Paul, Tony Shardlow, Neill D. F. Campbell

Keywords: Shape Interpolation, Shape Registration, 3D Articulated Shapes, Diffeomorphic Transformations, Neural Ordinary Differential Equations (NODEs), Geometric Measure Theory

TL;DR: A unified framework for unsupervised 3D shape interpolation and correspondence estimation using diffeomorphic transformations governed by a NODE and a simple skeleton structure, achieving state-of-the-art results across common datasets.

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, e.g physical priors.

Correspondence is recovered using an efficient Varifold formulation, that is effective on high-fidelity surfaces with differing parameterizations.

A simple skeleton structure augments the source shape, imposing physically motivated constraints on the deformation field and aiding in resolving symmetric ambiguities, without requiring skinning weights or 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.

Submission Number: 205