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arXiv · 2501.14038

Implicit Neural Surface Deformation with Explicit Velocity Fields

Lu Sang·Zehranaz Canfes·Dongliang Cao·Florian Bernard·Daniel Cremers
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Abstract

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.

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Lu Sang, Zehranaz Canfes, Dongliang Cao, Florian Bernard, Daniel Cremers. 2025-01-23. Implicit Neural Surface Deformation with Explicit Velocity Fields. https://arxiv.org/abs/2501.14038

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