# Endo-TSR: Temporal Spectral Modeling of Appearance and Motion for Endoscopic Reconstruction

arXiv: https://arxiv.org/abs/2609.32399 · HTML: https://mlsanity.com/paper/2609.32399/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 22 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [FoundationStereo: Zero-Shot Stereo Matching](https://mlsanity.com/paper/2501.09898/) (2025)
- [Neural Rendering for Stereo 3D Reconstruction of Deformable Tissues in Robotic Surgery](https://mlsanity.com/paper/2206.15255/) (2022)
- [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)
- [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)
- [Efficient Deformable Tissue Reconstruction via Orthogonal Neural Plane](https://mlsanity.com/paper/2312.15253/) (2023)
- [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)
- [EndoWave: 4D Gaussian Splatting with Rational Wavelet for Endoscopic Reconstruction](https://mlsanity.com/paper/2510.23087/) (2025)
- [GP-4DGS: Probabilistic 4D Gaussian Splatting from Monocular Video via Variational Gaussian Processes](https://mlsanity.com/paper/2604.02915/) (2026)

## Abstract (arXiv)

Endoscopic scene reconstruction requires modeling tissue motion and temporal appearance while recovering fine surface detail. Deformable Gaussian models provide explicit trajectories, but their fixed colour coefficients lack a dedicated temporal representation for photometric changes. We propose Endo-TSR, which augments deformable Gaussian splatting with bounded Fourier colour residuals and independent translation residuals on shared temporal frequencies. The colour residuals capture local appearance changes, while a Mat'ern spectral prior regularises motion corrections. Multi-scale Laplacian supervision guides tissue-detail recovery during joint image fitting. Extensive experiments on the EndoNeRF and StereoMIS datasets demonstrate state-of-the-art rendering quality, with the highest PSNR across all evaluated sequences. Ablation studies show that temporal appearance yields the largest PSNR gain among the tested component additions, while appearance and detail supervision jointly improve rendering with fixed Gaussian counts.