# Sparse Steerable Convolutions: An Efficient Learning of SE(3)-Equivariant Features for Estimation and Tracking of Object Poses in 3D Space

arXiv: https://arxiv.org/abs/2111.07383 · HTML: https://mlsanity.com/paper/2111.07383/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 27 references that are in the map.
- First posted on arXiv 14 Nov 2021.

## Builds on (most cited first, 22 of 22)

- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [PVNet: Pixel-wise Voting Network for 6DoF Pose Estimation](https://mlsanity.com/paper/1812.11788/) (2018)
- [DenseFusion: 6D Object Pose Estimation by Iterative Dense Fusion](https://mlsanity.com/paper/1901.04780/) (2019)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [SSD-6D: Making RGB-based 3D detection and 6D pose estimation great again](https://mlsanity.com/paper/1711.10006/) (2017)
- [Real-Time Seamless Single Shot 6D Object Pose Prediction](https://mlsanity.com/paper/1711.08848/) (2017)
- [PointFusion: Deep Sensor Fusion for 3D Bounding Box Estimation](https://mlsanity.com/paper/1711.10871/) (2017)
- [Implicit 3D Orientation Learning for 6D Object Detection from RGB Images](https://mlsanity.com/paper/1902.01275/) (2019)
- [Shape Prior Deformation for Categorical 6D Object Pose and Size Estimation](https://mlsanity.com/paper/2007.08454/) (2020)
- [Learning Canonical Shape Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/2001.09322/) (2020)
- [FS-Net: Fast Shape-based Network for Category-Level 6D Object Pose Estimation with Decoupled Rotation Mechanism](https://mlsanity.com/paper/2103.07054/) (2021)
- [DualPoseNet: Category-level 6D Object Pose and Size Estimation Using Dual Pose Network with Refined Learning of Pose Consistency](https://mlsanity.com/paper/2103.06526/) (2021)
- [6-PACK: Category-level 6D Pose Tracker with Anchor-Based Keypoints](https://mlsanity.com/paper/1910.10750/) (2019)
- [G2L-Net: Global to Local Network for Real-time 6D Pose Estimation with Embedding Vector Features](https://mlsanity.com/paper/2003.11089/) (2020)
- [Learning Analysis-by-Synthesis for 6D Pose Estimation in RGB-D Images](https://mlsanity.com/paper/1508.04546/) (2015)
- [Global Hypothesis Generation for 6D Object Pose Estimation](https://mlsanity.com/paper/1612.02287/) (2016)

## Built on by (most cited first, 17 of 17)

- [Gen6D: Generalizable Model-Free 6-DoF Object Pose Estimation from RGB Images](https://mlsanity.com/paper/2204.10776/) (2022)
- [SAM-6D: Segment Anything Model Meets Zero-Shot 6D Object Pose Estimation](https://mlsanity.com/paper/2311.15707/) (2023)
- [Category-Level 6D Object Pose and Size Estimation using Self-Supervised Deep Prior Deformation Networks](https://mlsanity.com/paper/2207.05444/) (2022)
- [SecondPose: SE(3)-Consistent Dual-Stream Feature Fusion for Category-Level Pose Estimation](https://mlsanity.com/paper/2311.11125/) (2023)
- [Transformation-Equivariant 3D Object Detection for Autonomous Driving](https://mlsanity.com/paper/2211.11962/) (2022)
- [VI-Net: Boosting Category-level 6D Object Pose Estimation via Learning Decoupled Rotations on the Spherical Representations](https://mlsanity.com/paper/2308.09916/) (2023)
- [3D molecule generation by denoising voxel grids](https://mlsanity.com/paper/2306.07473/) (2023)
- [Deep Learning-Based Object Pose Estimation: A Comprehensive Survey](https://mlsanity.com/paper/2405.07801/) (2024)
- [POPE: 6-DoF Promptable Pose Estimation of Any Object, in Any Scene, with One Reference](https://mlsanity.com/paper/2305.15727/) (2023)
- [Learning to Estimate 6DoF Pose from Limited Data: A Few-Shot, Generalizable Approach using RGB Images](https://mlsanity.com/paper/2306.07598/) (2023)
- [CLIPose: Category-Level Object Pose Estimation with Pre-trained Vision-Language Knowledge](https://mlsanity.com/paper/2402.15726/) (2024)
- [DCL-Net: Deep Correspondence Learning Network for 6D Pose Estimation](https://mlsanity.com/paper/2210.05232/) (2022)
- [Equivariant Single View Pose Prediction Via Induced and Restricted Representations](https://mlsanity.com/paper/2307.03704/) (2023)
- [SO(3)-Pose: SO(3)-Equivariance Learning for 6D Object Pose Estimation](https://mlsanity.com/paper/2208.08338/) (2022)
- [Lie Flow: Video Dynamic Fields Modeling and Predicting with Lie Algebra as Geometric Physics Principle](https://mlsanity.com/paper/2602.21645/) (2026)
- [Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space](https://mlsanity.com/paper/2605.15368/) (2026)
- [UniPose9D: Universal Category-Agnostic Object Pose Estimation](https://mlsanity.com/paper/2607.09985/) (2026)

## Abstract (arXiv)

As a basic component of SE(3)-equivariant deep feature learning, steerable convolution has recently demonstrated its advantages for 3D semantic analysis. The advantages are, however, brought by expensive computations on dense, volumetric data, which prevent its practical use for efficient processing of 3D data that are inherently sparse. In this paper, we propose a novel design of Sparse Steerable Convolution (SS-Conv) to address the shortcoming; SS-Conv greatly accelerates steerable convolution with sparse tensors, while strictly preserving the property of SE(3)-equivariance. Based on SS-Conv, we propose a general pipeline for precise estimation of object poses, wherein a key design is a Feature-Steering module that takes the full advantage of SE(3)-equivariance and is able to conduct an efficient pose refinement. To verify our designs, we conduct thorough experiments on three tasks of 3D object semantic analysis, including instance-level 6D pose estimation, category-level 6D pose and size estimation, and category-level 6D pose tracking. Our proposed pipeline based on SS-Conv outperforms existing methods on almost all the metrics evaluated by the three tasks. Ablation studies also show the superiority of our SS-Conv over alternative convolutions in terms of both accuracy and efficiency. Our code is released publicly at https://github.com/Gorilla-Lab-SCUT/SS-Conv.