# Surface Normal Estimation of Tilted Images via Spatial Rectifier

arXiv: https://arxiv.org/abs/2007.09264 · HTML: https://mlsanity.com/paper/2007.09264/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2020.

## Built on by (most cited first, 30 of 34)

- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimation](https://mlsanity.com/paper/2404.15506/) (2024)
- [StableNormal: Reducing Diffusion Variance for Stable and Sharp Normal](https://mlsanity.com/paper/2406.16864/) (2024)
- [Transformer-Based Attention Networks for Continuous Pixel-Wise Prediction](https://mlsanity.com/paper/2103.12091/) (2021)
- [NeuRIS: Neural Reconstruction of Indoor Scenes Using Normal Priors](https://mlsanity.com/paper/2206.13597/) (2022)
- [Rethinking Inductive Biases for Surface Normal Estimation](https://mlsanity.com/paper/2403.00712/) (2024)
- [Estimating and Exploiting the Aleatoric Uncertainty in Surface Normal Estimation](https://mlsanity.com/paper/2109.09881/) (2021)
- [Shape from Polarization for Complex Scenes in the Wild](https://mlsanity.com/paper/2112.11377/) (2021)
- [IronDepth: Iterative Refinement of Single-View Depth using Surface Normal and its Uncertainty](https://mlsanity.com/paper/2210.03676/) (2022)
- [NormalCrafter: Learning Temporally Consistent Normals from Video Diffusion Priors](https://mlsanity.com/paper/2504.11427/) (2025)
- [Deep Learning for Camera Calibration and Beyond: A Survey](https://mlsanity.com/paper/2303.10559/) (2023)
- [Neural LightRig: Unlocking Accurate Object Normal and Material Estimation with Multi-Light Diffusion](https://mlsanity.com/paper/2412.09593/) (2024)
- [PolyMaX: General Dense Prediction with Mask Transformer](https://mlsanity.com/paper/2311.05770/) (2023)
- [Towards Viewpoint Robustness in Bird's Eye View Segmentation](https://mlsanity.com/paper/2309.05192/) (2023)
- [Buffer Anytime: Zero-Shot Video Depth and Normal from Image Priors](https://mlsanity.com/paper/2411.17249/) (2024)
- [DejaVu: Conditional Regenerative Learning to Enhance Dense Prediction](https://mlsanity.com/paper/2303.01573/) (2023)
- [Deep Rotation Correction without Angle Prior](https://mlsanity.com/paper/2207.03054/) (2022)
- [Egocentric Scene Understanding via Multimodal Spatial Rectifier](https://mlsanity.com/paper/2207.07077/) (2022)
- [PanoNormal: Monocular Indoor 360deg Surface Normal Estimation](https://mlsanity.com/paper/2405.18745/) (2024)
- [VR-Drive: Viewpoint-Robust End-to-End Driving with Feed-Forward 3D Gaussian Splatting](https://mlsanity.com/paper/2510.23205/) (2025)
- [NeuralRoom: Geometry-Constrained Neural Implicit Surfaces for Indoor Scene Reconstruction](https://mlsanity.com/paper/2210.06853/) (2022)
- [DeepJoin: Learning a Joint Occupancy, Signed Distance, and Normal Field Function for Shape Repair](https://mlsanity.com/paper/2211.12400/) (2022)
- [Semi-Supervised Coupled Thin-Plate Spline Model for Rotation Correction and Beyond](https://mlsanity.com/paper/2401.13432/) (2024)
- [Multi-view Surface Reconstruction Using Normal and Reflectance Cues](https://mlsanity.com/paper/2506.04115/) (2025)
- [Improving Equivariance in State-of-the-Art Supervised Depth and Normal Predictors](https://mlsanity.com/paper/2309.16646/) (2023)
- [Multi-task Geometric Estimation of Depth and Surface Normal from Monocular 360deg Images](https://mlsanity.com/paper/2411.01749/) (2024)
- [Neural 3D Scene Reconstruction from Multiple 2D Images without 3D Supervision](https://mlsanity.com/paper/2306.17643/) (2023)
- [FOUND: Foot Optimization with Uncertain Normals for Surface Deformation Using Synthetic Data](https://mlsanity.com/paper/2310.18279/) (2023)
- [InfoNorm: Mutual Information Shaping of Normals for Sparse-View Reconstruction](https://mlsanity.com/paper/2407.12661/) (2024)
- [Monocular Normal Estimation via Shading Sequence Estimation](https://mlsanity.com/paper/2602.09929/) (2026)

## Abstract (arXiv)

In this paper, we present a spatial rectifier to estimate surface normals of tilted images. Tilted images are of particular interest as more visual data are captured by arbitrarily oriented sensors such as body-/robot-mounted cameras. Existing approaches exhibit bounded performance on predicting surface normals because they were trained using gravity-aligned images. Our two main hypotheses are: (1) visual scene layout is indicative of the gravity direction; and (2) not all surfaces are equally represented by a learned estimator due to the structured distribution of the training data, thus, there exists a transformation for each tilted image that is more responsive to the learned estimator than others. We design a spatial rectifier that is learned to transform the surface normal distribution of a tilted image to the rectified one that matches the gravity-aligned training data distribution. Along with the spatial rectifier, we propose a novel truncated angular loss that offers a stronger gradient at smaller angular errors and robustness to outliers. The resulting estimator outperforms the state-of-the-art methods including data augmentation baselines not only on ScanNet and NYUv2 but also on a new dataset called Tilt-RGBD that includes considerable roll and pitch camera motion.