# Eulerian Motion Reconstruction for Water Scenery

arXiv: https://arxiv.org/abs/2609.38622 · HTML: https://mlsanity.com/paper/2609.38622/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 45 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 34)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [SAM 3: Segment Anything with Concepts](https://mlsanity.com/paper/2511.16719/) (2025)
- [CoTracker: It is Better to Track Together](https://mlsanity.com/paper/2307.07635/) (2023)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [Mixture of Volumetric Primitives for Efficient Neural Rendering](https://mlsanity.com/paper/2103.01954/) (2021)
- [Triplane Meets Gaussian Splatting: Fast and Generalizable Single-View 3D Reconstruction with Transformers](https://mlsanity.com/paper/2312.09147/) (2023)
- [Shape of Motion: 4D Reconstruction from a Single Video](https://mlsanity.com/paper/2407.13764/) (2024)
- [MegaSaM: Accurate, Fast, and Robust Structure and Motion from Casual Dynamic Videos](https://mlsanity.com/paper/2412.04463/) (2024)
- [MoSca: Dynamic Gaussian Fusion from Casual Videos via 4D Motion Scaffolds](https://mlsanity.com/paper/2405.17421/) (2024)
- [L4GM: Large 4D Gaussian Reconstruction Model](https://mlsanity.com/paper/2406.10324/) (2024)
- [SV4D: Dynamic 3D Content Generation with Multi-Frame and Multi-View Consistency](https://mlsanity.com/paper/2407.17470/) (2024)
- [T"oRF: Time-of-Flight Radiance Fields for Dynamic Scene View Synthesis](https://mlsanity.com/paper/2109.15271/) (2021)
- [Animating Pictures with Eulerian Motion Fields](https://mlsanity.com/paper/2011.15128/) (2020)
- [4DGT: Learning a 4D Gaussian Transformer Using Real-World Monocular Videos](https://mlsanity.com/paper/2506.08015/) (2025)
- [Controllable Animation of Fluid Elements in Still Images](https://mlsanity.com/paper/2112.03051/) (2021)
- [MoVieS: Motion-Aware 4D Dynamic View Synthesis in One Second](https://mlsanity.com/paper/2507.10065/) (2025)
- [Vista4D: Video Reshooting with 4D Point Clouds](https://mlsanity.com/paper/2604.21915/) (2026)
- [Simulating Fluids in Real-World Still Images](https://mlsanity.com/paper/2204.11335/) (2022)
- [3D Moments from Near-Duplicate Photos](https://mlsanity.com/paper/2205.06255/) (2022)
- [DGS-LRM: Real-Time Deformable 3D Gaussian Reconstruction From Monocular Videos](https://mlsanity.com/paper/2506.09997/) (2025)
- [4D-LRM: Large Space-Time Reconstruction Model From and To Any View at Any Time](https://mlsanity.com/paper/2506.18890/) (2025)
- [Reconstruct, Inpaint, Test-Time Finetune: Dynamic Novel-view Synthesis from Monocular Videos](https://mlsanity.com/paper/2507.12646/) (2025)
- [Modeling Ambient Scene Dynamics for Free-view Synthesis](https://mlsanity.com/paper/2406.09395/) (2024)
- [Hardware-Rasterized Ray-Based Gaussian Splatting](https://mlsanity.com/paper/2503.18682/) (2025)

## Abstract (arXiv)

Reconstructing and animating water scenery from nature produces compelling and immersive visual experiences. Previous work examined this task from the perspective of 2D video textures, with the goal of creating a looping video. In our work, we tackle the problem from a 3D perspective, creating a looping 4D dynamic reconstruction which can be interactively rendered from novel viewpoints from a single non-looping 2D source video. We represent motion as a 3D static textitEulerian motion field that advects canonical Gaussian splats that are cyclically reborn at fixed time periods, supervised using rendering losses. To model non-periodic and stochastic dynamics present in real-world scenes, we add a non-periodic, time-varying residual term to capture deviations from the static Eulerian motion field. We show quantitatively and qualitatively that our framework enables photorealistic animation of water scenes better than prior art.