# Handling Object Symmetries in CNN-based Pose Estimation

arXiv: https://arxiv.org/abs/2011.13209 · HTML: https://mlsanity.com/paper/2011.13209/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2020.

## Built on by (most cited first, 8 of 8)

- [ZS6D: Zero-shot 6D Object Pose Estimation using Vision Transformers](https://mlsanity.com/paper/2309.11986/) (2023)
- [Challenges for Monocular 6D Object Pose Estimation in Robotics](https://mlsanity.com/paper/2307.12172/) (2023)
- [SyMFM6D: Symmetry-aware Multi-directional Fusion for Multi-View 6D Object Pose Estimation](https://mlsanity.com/paper/2307.00306/) (2023)
- [Open Challenges for Monocular Single-shot 6D Object Pose Estimation](https://mlsanity.com/paper/2302.11827/) (2023)
- [Resolving Symmetry Ambiguity in Correspondence-based Methods for Instance-level Object Pose Estimation](https://mlsanity.com/paper/2405.10557/) (2024)
- [Deep Measurement Updates for Bayes Filters](https://mlsanity.com/paper/2112.00380/) (2021)
- [ReFlow6D: Refraction-Guided Transparent Object 6D Pose Estimation via Intermediate Representation Learning](https://mlsanity.com/paper/2412.20830/) (2024)
- [Equivariant symmetry-aware head pose estimation for fetal MRI](https://mlsanity.com/paper/2512.04890/) (2025)

## Abstract (arXiv)

In this paper, we investigate the problems that Convolutional Neural Networks (CNN)-based pose estimators have with symmetric objects. We considered the value of the CNN's output representation when continuously rotating the object and found that it has to form a closed loop after each step of symmetry. Otherwise, the CNN (which is itself a continuous function) has to replicate an uncontinuous function. On a 1-DOF toy example we show that commonly used representations do not fulfill this demand and analyze the problems caused thereby. In particular, we find that the popular min-over-symmetries approach for creating a symmetry-aware loss tends not to work well with gradient-based optimization, i.e. deep learning. We propose a representation called "closed symmetry loop" (csl) from these insights, where the angle of relevant vectors is multiplied by the symmetry order and then generalize it to 6-DOF. The representation extends our algorithm from [Richter-Klug, ICVS, 2019] including a method to disambiguate symmetric equivalents during the final pose estimation. The algorithm handles continuous rotational symmetry (e.g. a bottle) and discrete rotational symmetry (e.g. a 4-fold symmetric box). It is evaluated on the T-LESS dataset, where it reaches state-of-the-art for unrefining RGB-based methods.