# EndoWave: 4D Gaussian Splatting with Rational Wavelet for Endoscopic Reconstruction

arXiv: https://arxiv.org/abs/2510.23087 · HTML: https://mlsanity.com/paper/2510.23087/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 26 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [GMFlow: Learning Optical Flow via Global Matching](https://mlsanity.com/paper/2111.13680/) (2021)
- [Neural Rendering for Stereo 3D Reconstruction of Deformable Tissues in Robotic Surgery](https://mlsanity.com/paper/2206.15255/) (2022)
- [Endo-Depth-and-Motion: Reconstruction and Tracking in Endoscopic Videos using Depth Networks and Photometric Constraints](https://mlsanity.com/paper/2103.16525/) (2021)
- [EndoSurf: Neural Surface Reconstruction of Deformable Tissues with Stereo Endoscope Videos](https://mlsanity.com/paper/2307.11307/) (2023)
- [Learning How To Robustly Estimate Camera Pose in Endoscopic Videos](https://mlsanity.com/paper/2304.08023/) (2023)
- [E-DSSR: Efficient Dynamic Surgical Scene Reconstruction with Transformer-based Stereoscopic Depth Perception](https://mlsanity.com/paper/2107.00229/) (2021)
- [Neural LerPlane Representations for Fast 4D Reconstruction of Deformable Tissues](https://mlsanity.com/paper/2305.19906/) (2023)
- [Endo-4DGS: Endoscopic Monocular Scene Reconstruction with 4D Gaussian Splatting](https://mlsanity.com/paper/2401.16416/) (2024)
- [Deform3DGS: Flexible Deformation for Fast Surgical Scene Reconstruction with Gaussian Splatting](https://mlsanity.com/paper/2405.17835/) (2024)
- [EndoGSLAM: Real-Time Dense Reconstruction and Tracking in Endoscopic Surgeries using Gaussian Splatting](https://mlsanity.com/paper/2403.15124/) (2024)
- [EndoGaussian: Real-time Gaussian Splatting for Dynamic Endoscopic Scene Reconstruction](https://mlsanity.com/paper/2401.12561/) (2024)
- [Free-SurGS: SfM-Free 3D Gaussian Splatting for Surgical Scene Reconstruction](https://mlsanity.com/paper/2407.02918/) (2024)
- [SurgicalGS: Dynamic 3D Gaussian Splatting for Accurate Robotic-Assisted Surgical Scene Reconstruction](https://mlsanity.com/paper/2410.09292/) (2024)
- [EndoFlow-SLAM: Real-Time Endoscopic SLAM with Flow-Constrained Gaussian Splatting](https://mlsanity.com/paper/2506.21420/) (2025)
- [UC-NeRF: Uncertainty-aware Conditional Neural Radiance Fields from Endoscopic Sparse Views](https://mlsanity.com/paper/2409.02917/) (2024)
- [A Review of 3D Reconstruction Techniques for Deformable Tissues in Robotic Surgery](https://mlsanity.com/paper/2408.04426/) (2024)
- [ULSR-GS: Ultra Large-scale Surface Reconstruction Gaussian Splatting with Multi-View Geometric Consistency](https://mlsanity.com/paper/2412.01402/) (2024)
- [Real-Time Spatio-Temporal Reconstruction of Dynamic Endoscopic Scenes with 4D Gaussian Splatting](https://mlsanity.com/paper/2411.01218/) (2024)

## Built on by (most cited first, 4 of 4)

- [Dental3R: Geometry-Aware Pairing for Intraoral 3D Reconstruction from Sparse-View Photographs](https://mlsanity.com/paper/2511.14315/) (2025)
- [G-SHARP: Gaussian Surgical Hardware Accelerated Real-time Pipeline](https://mlsanity.com/paper/2512.02482/) (2025)
- [DeGenseGS: Geometrically and Semantically Decoupled Surgical Scene Understanding in 4D Gaussian Splatting](https://mlsanity.com/paper/2607.04761/) (2026)
- [Endo-TSR: Temporal Spectral Modeling of Appearance and Motion for Endoscopic Reconstruction](https://mlsanity.com/paper/2609.32399/) (2026)

## Abstract (arXiv)

In robot-assisted minimally invasive surgery, accurate 3D reconstruction from endoscopic video is vital for downstream tasks and improved outcomes. However, endoscopic scenarios present unique challenges, including photometric inconsistencies, non-rigid tissue motion, and view-dependent highlights. Most 3DGS-based methods that rely solely on appearance constraints for optimizing 3DGS are often insufficient in this context, as these dynamic visual artifacts can mislead the optimization process and lead to inaccurate reconstructions. To address these limitations, we present EndoWave, a unified spatio-temporal Gaussian Splatting framework by incorporating an optical flow-based geometric constraint and a multi-resolution rational wavelet supervision. First, we adopt a unified spatio-temporal Gaussian representation that directly optimizes primitives in a 4D domain. Second, we propose a geometric constraint derived from optical flow to enhance temporal coherence and effectively constrain the 3D structure of the scene. Third, we propose a multi-resolution rational orthogonal wavelet as a constraint, which can effectively separate the details of the endoscope and enhance the rendering performance. Extensive evaluations on two real surgical datasets, EndoNeRF and StereoMIS, demonstrate that our method EndoWave achieves state-of-the-art reconstruction quality and visual accuracy compared to the baseline method.