In this work, we introduce the first unsupervised method that simultaneously predicts time-varying neural implicit surfaces and deformations between pairs of point clouds. We propose to model the point movement using an explicit velocity field and directly deform a time-varying implicit field using the modified level-set equation. This equation utilizes an iso-surface evolution with Eikonal constraints in a compact formulation, ensuring the integrity of the signed distance field. By applying a smooth, volume-preserving constraint to the velocity field, our method successfully recovers physically plausible intermediate shapes. Our method is able to handle both rigid and non-rigid deformations without any intermediate shape supervision. Our experimental results demonstrate that our method significantly outperforms existing works, delivering superior results in both quality and efficiency.
@article{arxiv.2501.14038,
title = {Implicit Neural Surface Deformation with Explicit Velocity Fields},
author = {Lu Sang and Zehranaz Canfes and Dongliang Cao and Florian Bernard and Daniel Cremers},
journal= {arXiv preprint arXiv:2501.14038},
year = {2025}
}