# Learning Unorthogonalized Matrices for Rotation Estimation

arXiv: https://arxiv.org/abs/2312.00462 · HTML: https://mlsanity.com/paper/2312.00462/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 39 references that are in the map.
- First posted on arXiv 1 Dec 2023.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [End-to-end Recovery of Human Shape and Pose](https://mlsanity.com/paper/1712.06584/) (2017)
- [Learning to Reconstruct 3D Human Pose and Shape via Model-fitting in the Loop](https://mlsanity.com/paper/1909.12828/) (2019)
- [VIBE: Video Inference for Human Body Pose and Shape Estimation](https://mlsanity.com/paper/1912.05656/) (2019)
- [Monocular 3D Human Pose Estimation In The Wild Using Improved CNN Supervision](https://mlsanity.com/paper/1611.09813/) (2016)
- [ViTPose: Simple Vision Transformer Baselines for Human Pose Estimation](https://mlsanity.com/paper/2204.12484/) (2022)
- [End-to-End Human Pose and Mesh Reconstruction with Transformers](https://mlsanity.com/paper/2012.09760/) (2020)
- [Learning joint reconstruction of hands and manipulated objects](https://mlsanity.com/paper/1904.05767/) (2019)
- [PARE: Part Attention Regressor for 3D Human Body Estimation](https://mlsanity.com/paper/2104.08527/) (2021)
- [HybrIK: A Hybrid Analytical-Neural Inverse Kinematics Solution for 3D Human Pose and Shape Estimation](https://mlsanity.com/paper/2011.14672/) (2020)
- [I2L-MeshNet: Image-to-Lixel Prediction Network for Accurate 3D Human Pose and Mesh Estimation from a Single RGB Image](https://mlsanity.com/paper/2008.03713/) (2020)
- [FreiHAND: A Dataset for Markerless Capture of Hand Pose and Shape from Single RGB Images](https://mlsanity.com/paper/1909.04349/) (2019)
- [InterHand2.6M: A Dataset and Baseline for 3D Interacting Hand Pose Estimation from a Single RGB Image](https://mlsanity.com/paper/2008.09309/) (2020)
- [CLIFF: Carrying Location Information in Full Frames into Human Pose and Shape Estimation](https://mlsanity.com/paper/2208.00571/) (2022)
- [AGORA: Avatars in Geography Optimized for Regression Analysis](https://mlsanity.com/paper/2104.14643/) (2021)
- [Beyond Static Features for Temporally Consistent 3D Human Pose and Shape from a Video](https://mlsanity.com/paper/2011.08627/) (2020)
- [Exemplar Fine-Tuning for 3D Human Model Fitting Towards In-the-Wild 3D Human Pose Estimation](https://mlsanity.com/paper/2004.03686/) (2020)
- [How Does Information Bottleneck Help Deep Learning?](https://mlsanity.com/paper/2305.18887/) (2023)
- [An Analysis of SVD for Deep Rotation Estimation](https://mlsanity.com/paper/2006.14616/) (2020)
- [On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems](https://mlsanity.com/paper/2006.11144/) (2020)
- [Convergence rates for the stochastic gradient descent method for non-convex objective functions](https://mlsanity.com/paper/1904.01517/) (2019)
- [Stochastic Gradient Descent for Nonconvex Learning without Bounded Gradient Assumptions](https://mlsanity.com/paper/1902.00908/) (2019)
- [Robust Differentiable SVD](https://mlsanity.com/paper/2104.03821/) (2021)
- [Depth with Nonlinearity Creates No Bad Local Minima in ResNets](https://mlsanity.com/paper/1810.09038/) (2018)
- [Understanding Dynamics of Nonlinear Representation Learning and Its Application](https://mlsanity.com/paper/2106.14836/) (2021)

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

- [KITRO: Refining Human Mesh by 2D Clues and Kinematic-tree Rotation](https://mlsanity.com/paper/2405.19833/) (2024)
- [Training Without Orthogonalization, Inference With SVD: A Gradient Analysis of Rotation Representations](https://mlsanity.com/paper/2604.05414/) (2026)
- [Revisiting Euler-Angle Regression with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2607.09650/) (2026)

## Abstract (arXiv)

Estimating 3D rotations is a common procedure for 3D computer vision. The accuracy depends heavily on the rotation representation. One form of representation -- rotation matrices -- is popular due to its continuity, especially for pose estimation tasks. The learning process usually incorporates orthogonalization to ensure orthonormal matrices. Our work reveals, through gradient analysis, that common orthogonalization procedures based on the Gram-Schmidt process and singular value decomposition will slow down training efficiency. To this end, we advocate removing orthogonalization from the learning process and learning unorthogonalized `Pseudo' Rotation Matrices (PRoM). An optimization analysis shows that PRoM converges faster and to a better solution. By replacing the orthogonalization incorporated representation with our proposed PRoM in various rotation-related tasks, we achieve state-of-the-art results on large-scale benchmarks for human pose estimation.