# Implicit Neural Surface Deformation with Explicit Velocity Fields

arXiv: https://arxiv.org/abs/2501.14038 · HTML: https://mlsanity.com/paper/2501.14038/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2025.

## Built on by (most cited first, 6 of 6)

- [4Deform: Neural Surface Deformation for Robust Shape Interpolation](https://mlsanity.com/paper/2502.20208/) (2025)
- [TwoSquared: 4D Generation from 2D Image Pairs](https://mlsanity.com/paper/2504.12825/) (2025)
- [FLOWING: Implicit Neural Flows for Structure-Preserving Morphing](https://mlsanity.com/paper/2510.09537/) (2025)
- [GENIE: Gram-Eigenmode INR Editing with Closed-Form Geometry Updates](https://mlsanity.com/paper/2603.29860/) (2026)
- [NeuralSRNF: Neural Square Root Normal Fields for the Statistical Shape Analysis and Generation of Nonrigid 3D and 4D Objects](https://mlsanity.com/paper/2609.27728/) (2026)
- [M-plicits: Neural Implicit Surfaces via Nested Multiscale Residuals](https://mlsanity.com/paper/2609.28684/) (2026)

## Abstract (arXiv)

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.