# Dynamical Pose Estimation

arXiv: https://arxiv.org/abs/2103.06182 · HTML: https://mlsanity.com/paper/2103.06182/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 72 references that are in the map.
- First posted on arXiv 10 Mar 2021.

## Builds on (most cited first, 29 of 29)

- [Learning to Reconstruct 3D Human Pose and Shape via Model-fitting in the Loop](https://mlsanity.com/paper/1909.12828/) (2019)
- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age](https://mlsanity.com/paper/1606.05830/) (2016)
- [PVNet: Pixel-wise Voting Network for 6DoF Pose Estimation](https://mlsanity.com/paper/1812.11788/) (2018)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Kimera: an Open-Source Library for Real-Time Metric-Semantic Localization and Mapping](https://mlsanity.com/paper/1910.02490/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [kPAM: KeyPoint Affordances for Category-Level Robotic Manipulation](https://mlsanity.com/paper/1903.06684/) (2019)
- [A robust self-learning method for fully unsupervised cross-lingual mappings of word embeddings](https://mlsanity.com/paper/1805.06297/) (2018)
- [Deep MANTA: A Coarse-to-fine Many-Task Network for joint 2D and 3D vehicle analysis from monocular image](https://mlsanity.com/paper/1703.07570/) (2017)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [Supervised Fitting of Geometric Primitives to 3D Point Clouds](https://mlsanity.com/paper/1811.08988/) (2018)
- [Satellite Pose Estimation with Deep Landmark Regression and Nonlinear Pose Refinement](https://mlsanity.com/paper/1908.11542/) (2019)
- [A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates](https://mlsanity.com/paper/1903.08588/) (2019)
- [A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers](https://mlsanity.com/paper/1905.12536/) (2019)
- [GSNet: Joint Vehicle Pose and Shape Reconstruction with Geometrical and Scene-aware Supervision](https://mlsanity.com/paper/2007.13124/) (2020)
- [Outlier-Robust Estimation: Hardness, Minimally Tuned Algorithms, and Applications](https://mlsanity.com/paper/2007.15109/) (2020)
- [Self-supervised Geometric Perception](https://mlsanity.com/paper/2103.03114/) (2021)
- [Pose Estimation for Non-Cooperative Rendezvous Using Neural Networks](https://mlsanity.com/paper/1906.09868/) (2019)
- [One Ring to Rule Them All: Certifiably Robust Geometric Perception with Outliers](https://mlsanity.com/paper/2006.06769/) (2020)
- [In Perfect Shape: Certifiably Optimal 3D Shape Reconstruction from 2D Landmarks](https://mlsanity.com/paper/1911.11924/) (2019)
- [Sparse Representation for 3D Shape Estimation: A Convex Relaxation Approach](https://mlsanity.com/paper/1509.04309/) (2015)
- [CvxPnPL: A Unified Convex Solution to the Absolute Pose Estimation Problem from Point and Line Correspondences](https://mlsanity.com/paper/1907.10545/) (2019)
- [3D Shape Estimation from 2D Landmarks: A Convex Relaxation Approach](https://mlsanity.com/paper/1411.2942/) (2014)
- [Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations](https://mlsanity.com/paper/2009.14005/) (2020)
- [A Dynamical Perspective on Point Cloud Registration](https://mlsanity.com/paper/2005.03190/) (2020)

## Built on by (most cited first, 6 of 6)

- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [Estimation Contracts for Outlier-Robust Geometric Perception](https://mlsanity.com/paper/2208.10521/) (2022)
- [Optimal and Robust Category-level Perception: Object Pose and Shape Estimation from 2D and 3D Semantic Keypoints](https://mlsanity.com/paper/2206.12498/) (2022)
- [Semi-automatic 3D Object Keypoint Annotation and Detection for the Masses](https://mlsanity.com/paper/2201.07665/) (2022)
- [The Determinant Ratio Matrix Approach to Solving 3D Matching and 2D Orthographic Projection Alignment Tasks](https://mlsanity.com/paper/2511.19511/) (2025)
- [Learning Manifold and Ito Dynamics with Branched Neural Rough Differential Equations](https://mlsanity.com/paper/2606.05272/) (2026)

## Abstract (arXiv)

We study the problem of aligning two sets of 3D geometric primitives given known correspondences. Our first contribution is to show that this primitive alignment framework unifies five perception problems including point cloud registration, primitive (mesh) registration, category-level 3D registration, absolution pose estimation (APE), and category-level APE. Our second contribution is to propose DynAMical Pose estimation (DAMP), the first general and practical algorithm to solve primitive alignment problem by simulating rigid body dynamics arising from virtual springs and damping, where the springs span the shortest distances between corresponding primitives. We evaluate DAMP in simulated and real datasets across all five problems, and demonstrate (i) DAMP always converges to the globally optimal solution in the first three problems with 3D-3D correspondences; (ii) although DAMP sometimes converges to suboptimal solutions in the last two problems with 2D-3D correspondences, using a scheme for escaping local minima, DAMP always succeeds. Our third contribution is to demystify the surprising empirical performance of DAMP and formally prove a global convergence result in the case of point cloud registration by charactering local stability of the equilibrium points of the underlying dynamical system.