# Towards Understanding 3D Vision: the Role of Gaussian Curvature

arXiv: https://arxiv.org/abs/2508.11825 · HTML: https://mlsanity.com/paper/2508.11825/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 15 Aug 2025.

## Builds on (most cited first, 12 of 12)

- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [Depth Pro: Sharp Monocular Metric Depth in Less Than a Second](https://mlsanity.com/paper/2410.02073/) (2024)
- [RAFT-Stereo: Multilevel Recurrent Field Transforms for Stereo Matching](https://mlsanity.com/paper/2109.07547/) (2021)
- [Practical Stereo Matching via Cascaded Recurrent Network with Adaptive Correlation](https://mlsanity.com/paper/2203.11483/) (2022)
- [FoundationStereo: Zero-Shot Stereo Matching](https://mlsanity.com/paper/2501.09898/) (2025)
- [Selective-Stereo: Adaptive Frequency Information Selection for Stereo Matching](https://mlsanity.com/paper/2403.00486/) (2024)
- [DEFOM-Stereo: Depth Foundation Model Based Stereo Matching](https://mlsanity.com/paper/2501.09466/) (2025)
- [SAGS: Structure-Aware 3D Gaussian Splatting](https://mlsanity.com/paper/2404.19149/) (2024)
- [MonSter++: Unified Stereo Matching, Multi-view Stereo, and Real-time Stereo with Monodepth Priors](https://mlsanity.com/paper/2501.08643/) (2025)
- [All-in-One: Transferring Vision Foundation Models into Stereo Matching](https://mlsanity.com/paper/2412.09912/) (2024)
- [NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature](https://mlsanity.com/paper/2404.13420/) (2024)

## Abstract (arXiv)

Recent advances in computer vision have predominantly relied on data-driven approaches that leverage deep learning and large-scale datasets. Deep neural networks have achieved remarkable success in tasks such as stereo matching and monocular depth reconstruction. However, these methods lack explicit models of 3D geometry that can be directly analyzed, transferred across modalities, or systematically modified for controlled experimentation. We investigate the role of Gaussian curvature in 3D surface modeling. Besides Gaussian curvature being an invariant quantity under change of observers or coordinate systems, we demonstrate using the Middlebury stereo dataset that it offers a sparse and compact description of 3D surfaces. Furthermore, we show a strong correlation between the performance rank of top state-of-the-art stereo and monocular methods and the low total absolute Gaussian curvature. We propose that this property can serve as a geometric prior to improve future 3D reconstruction algorithms.