# Learning Implicit Probability Distribution Functions for Symmetric Orientation Estimation from RGB Images Without Pose Labels

arXiv: https://arxiv.org/abs/2211.11394 · HTML: https://mlsanity.com/paper/2211.11394/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 45 references that are in the map.
- First posted on arXiv 21 Nov 2022.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [RefineNet: Multi-Path Refinement Networks for High-Resolution Semantic Segmentation](https://mlsanity.com/paper/1611.06612/) (2016)
- [CosyPose: Consistent multi-view multi-object 6D pose estimation](https://mlsanity.com/paper/2008.08465/) (2020)
- [BB8: A Scalable, Accurate, Robust to Partial Occlusion Method for Predicting the 3D Poses of Challenging Objects without Using Depth](https://mlsanity.com/paper/1703.10896/) (2017)
- [BOP Challenge 2020 on 6D Object Localization](https://mlsanity.com/paper/2009.07378/) (2020)
- [Explaining the Ambiguity of Object Detection and 6D Pose From Visual Data](https://mlsanity.com/paper/1812.00287/) (2018)
- [Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold](https://mlsanity.com/paper/2106.05965/) (2021)
- [Deep Directional Statistics: Pose Estimation with Uncertainty Quantification](https://mlsanity.com/paper/1805.03430/) (2018)
- [Deep Bingham Networks: Dealing with Uncertainty and Ambiguity in Pose Estimation](https://mlsanity.com/paper/2012.11002/) (2020)
- [RNNPose: Recurrent 6-DoF Object Pose Refinement with Robust Correspondence Field Estimation and Pose Optimization](https://mlsanity.com/paper/2203.12870/) (2022)
- [Probabilistic orientation estimation with matrix Fisher distributions](https://mlsanity.com/paper/2006.09740/) (2020)
- [On Object Symmetries and 6D Pose Estimation from Images](https://mlsanity.com/paper/1908.07640/) (2019)
- [RGB-D Object Detection and Semantic Segmentation for Autonomous Manipulation in Clutter](https://mlsanity.com/paper/1810.00818/) (2018)
- [Defining the Pose of any 3D Rigid Object and an Associated Distance](https://mlsanity.com/paper/1612.04631/) (2016)
- [Learning Orientation Distributions for Object Pose Estimation](https://mlsanity.com/paper/2007.01418/) (2020)
- [YOLOPose: Transformer-based Multi-Object 6D Pose Estimation using Keypoint Regression](https://mlsanity.com/paper/2205.02536/) (2022)
- [Pose Estimation for Objects with Rotational Symmetry](https://mlsanity.com/paper/1810.05780/) (2018)
- [Cross-Domain 3D Equivariant Image Embeddings](https://mlsanity.com/paper/1812.02716/) (2018)
- [Robust 6D Object Pose Estimation in Cluttered Scenes using Semantic Segmentation and Pose Regression Networks](https://mlsanity.com/paper/1810.03410/) (2018)

## Built on by (most cited first, 2 of 2)

- [BOP-Distrib: Revisiting 6D Pose Estimation Benchmarks for Better Evaluation under Visual Ambiguities](https://mlsanity.com/paper/2408.17297/) (2024)
- [Towards Symmetry-sensitive Pose Estimation: A Rotation Representation for Symmetric Object Classes](https://mlsanity.com/paper/2604.18208/) (2026)

## Abstract (arXiv)

Object pose estimation is a necessary prerequisite for autonomous robotic manipulation, but the presence of symmetry increases the complexity of the pose estimation task. Existing methods for object pose estimation output a single 6D pose. Thus, they lack the ability to reason about symmetries. Lately, modeling object orientation as a non-parametric probability distribution on the SO(3) manifold by neural networks has shown impressive results. However, acquiring large-scale datasets to train pose estimation models remains a bottleneck. To address this limitation, we introduce an automatic pose labeling scheme. Given RGB-D images without object pose annotations and 3D object models, we design a two-stage pipeline consisting of point cloud registration and render-and-compare validation to generate multiple symmetrical pseudo-ground-truth pose labels for each image. Using the generated pose labels, we train an ImplicitPDF model to estimate the likelihood of an orientation hypothesis given an RGB image. An efficient hierarchical sampling of the SO(3) manifold enables tractable generation of the complete set of symmetries at multiple resolutions. During inference, the most likely orientation of the target object is estimated using gradient ascent. We evaluate the proposed automatic pose labeling scheme and the ImplicitPDF model on a photorealistic dataset and the T-Less dataset, demonstrating the advantages of the proposed method.