# Laplacian Analysis Meets Dynamics Modelling: Gaussian Splatting for 4D Reconstruction

arXiv: https://arxiv.org/abs/2508.04966 · HTML: https://mlsanity.com/paper/2508.04966/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 40 references that are in the map.
- First posted on arXiv 7 Aug 2025.

## Builds on (most cited first, 25 of 25)

- [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)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Block-NeRF: Scalable Large Scene Neural View Synthesis](https://mlsanity.com/paper/2202.05263/) (2022)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (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)
- [PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics](https://mlsanity.com/paper/2311.12198/) (2023)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [Tensor4D : Efficient Neural 4D Decomposition for High-fidelity Dynamic Reconstruction and Rendering](https://mlsanity.com/paper/2211.11610/) (2022)
- [Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle](https://mlsanity.com/paper/2312.03431/) (2023)
- [BANMo: Building Animatable 3D Neural Models from Many Casual Videos](https://mlsanity.com/paper/2112.12761/) (2021)
- [3D Geometry-aware Deformable Gaussian Splatting for Dynamic View Synthesis](https://mlsanity.com/paper/2404.06270/) (2024)
- [Grid4D: 4D Decomposed Hash Encoding for High-Fidelity Dynamic Gaussian Splatting](https://mlsanity.com/paper/2410.20815/) (2024)
- [SplineGS: Robust Motion-Adaptive Spline for Real-Time Dynamic 3D Gaussians from Monocular Video](https://mlsanity.com/paper/2412.09982/) (2024)
- [Semantic Attention Flow Fields for Monocular Dynamic Scene Decomposition](https://mlsanity.com/paper/2303.01526/) (2023)

## Abstract (arXiv)

While 3D Gaussian Splatting (3DGS) excels in static scene modeling, its extension to dynamic scenes introduces significant challenges. Existing dynamic 3DGS methods suffer from either over-smoothing due to low-rank decomposition or feature collision from high-dimensional grid sampling. This is because of the inherent spectral conflicts between preserving motion details and maintaining deformation consistency at different frequency. To address these challenges, we propose a novel dynamic 3DGS framework with hybrid explicit-implicit functions. Our approach contains three key innovations: a spectral-aware Laplacian encoding architecture which merges Hash encoding and Laplacian-based module for flexible frequency motion control, an enhanced Gaussian dynamics attribute that compensates for photometric distortions caused by geometric deformation, and an adaptive Gaussian split strategy guided by KDTree-based primitive control to efficiently query and optimize dynamic areas. Through extensive experiments, our method demonstrates state-of-the-art performance in reconstructing complex dynamic scenes, achieving better reconstruction fidelity.