# SDA-SNE: Spatial Discontinuity-Aware Surface Normal Estimation via Multi-Directional Dynamic Programming

arXiv: https://arxiv.org/abs/2208.08667 · HTML: https://mlsanity.com/paper/2208.08667/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 18 Aug 2022.

## Builds on (most cited first, 4 of 4)

- [SNE-RoadSeg: Incorporating Surface Normal Information into Semantic Segmentation for Accurate Freespace Detection](https://mlsanity.com/paper/2008.11351/) (2020)
- [Pothole Detection Based on Disparity Transformation and Road Surface Modeling](https://mlsanity.com/paper/1908.00894/) (2019)
- [SNE-RoadSeg+: Rethinking Depth-Normal Translation and Deep Supervision for Freespace Detection](https://mlsanity.com/paper/2107.14599/) (2021)
- [Three-Filters-to-Normal: An Accurate and Ultrafast Surface Normal Estimator](https://mlsanity.com/paper/2005.08165/) (2020)

## Built on by (most cited first, 3 of 3)

- [D2NT: A High-Performing Depth-to-Normal Translator](https://mlsanity.com/paper/2304.12031/) (2023)
- [Three-Filters-to-Normal+: Revisiting Discontinuity Discrimination in Depth-to-Normal Translation](https://mlsanity.com/paper/2312.07964/) (2023)
- [Robust and Real-time Surface Normal Estimation from Stereo Disparities using Affine Transformations](https://mlsanity.com/paper/2504.15121/) (2025)

## Abstract (arXiv)

The state-of-the-art (SoTA) surface normal estimators (SNEs) generally translate depth images into surface normal maps in an end-to-end fashion. Although such SNEs have greatly minimized the trade-off between efficiency and accuracy, their performance on spatial discontinuities, e.g., edges and ridges, is still unsatisfactory. To address this issue, this paper first introduces a novel multi-directional dynamic programming strategy to adaptively determine inliers (co-planar 3D points) by minimizing a (path) smoothness energy. The depth gradients can then be refined iteratively using a novel recursive polynomial interpolation algorithm, which helps yield more reasonable surface normals. Our introduced spatial discontinuity-aware (SDA) depth gradient refinement strategy is compatible with any depth-to-normal SNEs. Our proposed SDA-SNE achieves much greater performance than all other SoTA approaches, especially near/on spatial discontinuities. We further evaluate the performance of SDA-SNE with respect to different iterations, and the results suggest that it converges fast after only a few iterations. This ensures its high efficiency in various robotics and computer vision applications requiring real-time performance. Additional experiments on the datasets with different extents of random noise further validate our SDA-SNE's robustness and environmental adaptability. Our source code, demo video, and supplementary material are publicly available at mias.group/SDA-SNE.