# Robust and Real-time Surface Normal Estimation from Stereo Disparities using Affine Transformations

arXiv: https://arxiv.org/abs/2504.15121 · HTML: https://mlsanity.com/paper/2504.15121/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 21 Apr 2025.

## Builds on (most cited first, 18 of 18)

- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [Predicting Depth, Surface Normals and Semantic Labels with a Common Multi-Scale Convolutional Architecture](https://mlsanity.com/paper/1411.4734/) (2014)
- [Learning a Multi-View Stereo Machine](https://mlsanity.com/paper/1708.05375/) (2017)
- [Point-Based Multi-View Stereo Network](https://mlsanity.com/paper/1908.04422/) (2019)
- [MeshLoc: Mesh-Based Visual Localization](https://mlsanity.com/paper/2207.10762/) (2022)
- [Designing Deep Networks for Surface Normal Estimation](https://mlsanity.com/paper/1411.4958/) (2014)
- [Bilateral Grid Learning for Stereo Matching Networks](https://mlsanity.com/paper/2101.01601/) (2021)
- [Large-scale, real-time visual-inertial localization revisited](https://mlsanity.com/paper/1907.00338/) (2019)
- [Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm](https://mlsanity.com/paper/1906.02290/) (2019)
- [Toward Geometric Deep SLAM](https://mlsanity.com/paper/1707.07410/) (2017)
- [Marr Revisited: 2D-3D Alignment via Surface Normal Prediction](https://mlsanity.com/paper/1604.01347/) (2016)
- [Multi-Class Model Fitting by Energy Minimization and Mode-Seeking](https://mlsanity.com/paper/1706.00827/) (2017)
- [Three-Filters-to-Normal: An Accurate and Ultrafast Surface Normal Estimator](https://mlsanity.com/paper/2005.08165/) (2020)
- [Efficient Initial Pose-graph Generation for Global SfM](https://mlsanity.com/paper/2011.11986/) (2020)
- [D2NT: A High-Performing Depth-to-Normal Translator](https://mlsanity.com/paper/2304.12031/) (2023)
- [Self-supervised Learning for Single View Depth and Surface Normal Estimation](https://mlsanity.com/paper/1903.00112/) (2019)
- [SDA-SNE: Spatial Discontinuity-Aware Surface Normal Estimation via Multi-Directional Dynamic Programming](https://mlsanity.com/paper/2208.08667/) (2022)

## Built on by (most cited first, 1 of 1)

- [A Unified Formula for Affine Transformations between Calibrated Cameras](https://mlsanity.com/paper/2602.06805/) (2026)

## Abstract (arXiv)

This work introduces a novel method for surface normal estimation from rectified stereo image pairs, leveraging affine transformations derived from disparity values to achieve fast and accurate results. We demonstrate how the rectification of stereo image pairs simplifies the process of surface normal estimation by reducing computational complexity. To address noise reduction, we develop a custom algorithm inspired by convolutional operations, tailored to process disparity data efficiently. We also introduce adaptive heuristic techniques for efficiently detecting connected surface components within the images, further improving the robustness of the method. By integrating these methods, we construct a surface normal estimator that is both fast and accurate, producing a dense, oriented point cloud as the final output. Our method is validated using both simulated environments and real-world stereo images from the Middlebury and Cityscapes datasets, demonstrating significant improvements in real-time performance and accuracy when implemented on a GPU. Upon acceptance, the shader source code will be made publicly available to facilitate further research and reproducibility.