# An Analysis of SVD for Deep Rotation Estimation

arXiv: https://arxiv.org/abs/2006.14616 · HTML: https://mlsanity.com/paper/2006.14616/

## Key facts

- Cited by 86 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2020.

## Built on by (most cited first, 30 of 86)

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- [DexGraspNet 2.0: Learning Generative Dexterous Grasping in Large-scale Synthetic Cluttered Scenes](https://mlsanity.com/paper/2410.23004/) (2024)
- [Extreme Rotation Estimation using Dense Correlation Volumes](https://mlsanity.com/paper/2104.13530/) (2021)
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- [Projective Manifold Gradient Layer for Deep Rotation Regression](https://mlsanity.com/paper/2110.11657/) (2021)
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- [FisherMatch: Semi-Supervised Rotation Regression via Entropy-based Filtering](https://mlsanity.com/paper/2203.15765/) (2022)
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## Abstract (arXiv)

Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto O(n) or SO(n). These tools have long been used for applications in computer vision, for example optimal 3D alignment problems solved by orthogonal Procrustes, rotation averaging, or Essential matrix decomposition. Despite its utility in different settings, SVD orthogonalization as a procedure for producing rotation matrices is typically overlooked in deep learning models, where the preferences tend toward classic representations like unit quaternions, Euler angles, and axis-angle, or more recently-introduced methods. Despite the importance of 3D rotations in computer vision and robotics, a single universally effective representation is still missing. Here, we explore the viability of SVD orthogonalization for 3D rotations in neural networks. We present a theoretical analysis that shows SVD is the natural choice for projecting onto the rotation group. Our extensive quantitative analysis shows simply replacing existing representations with the SVD orthogonalization procedure obtains state of the art performance in many deep learning applications covering both supervised and unsupervised training.