# 4D Panoptic Segmentation as Invariant and Equivariant Field Prediction

arXiv: https://arxiv.org/abs/2303.15651 · HTML: https://mlsanity.com/paper/2303.15651/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 58 references that are in the map.
- First posted on arXiv 28 Mar 2023.

## Builds on (most cited first, 30 of 48)

- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [PointPillars: Fast Encoders for Object Detection from Point Clouds](https://mlsanity.com/paper/1812.05784/) (2018)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Panoptic Segmentation](https://mlsanity.com/paper/1801.00868/) (2018)
- [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)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Panoptic nuScenes: A Large-Scale Benchmark for LiDAR Panoptic Segmentation and Tracking](https://mlsanity.com/paper/2109.03805/) (2021)
- [Seamless Scene Segmentation](https://mlsanity.com/paper/1905.01220/) (2019)
- [EfficientPS: Efficient Panoptic Segmentation](https://mlsanity.com/paper/2004.02307/) (2020)
- [Panoptic-PolarNet: Proposal-free LiDAR Point Cloud Panoptic Segmentation](https://mlsanity.com/paper/2103.14962/) (2021)
- [3D Object Detection for Autonomous Driving: A Survey](https://mlsanity.com/paper/2106.10823/) (2021)
- [Just Go with the Flow: Self-Supervised Scene Flow Estimation](https://mlsanity.com/paper/1912.00497/) (2019)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [LiDAR-based Panoptic Segmentation via Dynamic Shifting Network](https://mlsanity.com/paper/2011.11964/) (2020)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [EfficientLPS: Efficient LiDAR Panoptic Segmentation](https://mlsanity.com/paper/2102.08009/) (2021)
- [4D Panoptic LiDAR Segmentation](https://mlsanity.com/paper/2102.12472/) (2021)
- [InverseForm: A Loss Function for Structured Boundary-Aware Segmentation](https://mlsanity.com/paper/2104.02745/) (2021)
- [DeeperLab: Single-Shot Image Parser](https://mlsanity.com/paper/1902.05093/) (2019)
- [Panoptic-PHNet: Towards Real-Time and High-Precision LiDAR Panoptic Segmentation via Clustering Pseudo Heatmap](https://mlsanity.com/paper/2205.07002/) (2022)
- [MOPT: Multi-Object Panoptic Tracking](https://mlsanity.com/paper/2004.08189/) (2020)
- [Transformation-Equivariant 3D Object Detection for Autonomous Driving](https://mlsanity.com/paper/2211.11962/) (2022)

## Built on by (most cited first, 19 of 19)

- [Better Call SAL: Towards Learning to Segment Anything in Lidar](https://mlsanity.com/paper/2403.13129/) (2024)
- [Equivariant plug-and-play image reconstruction](https://mlsanity.com/paper/2312.01831/) (2023)
- [Mask4Former: Mask Transformer for 4D Panoptic Segmentation](https://mlsanity.com/paper/2309.16133/) (2023)
- [TASeg: Temporal Aggregation Network for LiDAR Semantic Segmentation](https://mlsanity.com/paper/2407.09751/) (2024)
- [4D-Former: Multimodal 4D Panoptic Segmentation](https://mlsanity.com/paper/2311.01520/) (2023)
- [Lie Neurons: Adjoint-Equivariant Neural Networks for Semisimple Lie Algebras](https://mlsanity.com/paper/2310.04521/) (2023)
- [ZOPP: A Framework of Zero-shot Offboard Panoptic Perception for Autonomous Driving](https://mlsanity.com/paper/2411.05311/) (2024)
- [Zero-Shot 4D Lidar Panoptic Segmentation](https://mlsanity.com/paper/2504.00848/) (2025)
- [Interactive4D: Interactive 4D LiDAR Segmentation](https://mlsanity.com/paper/2410.08206/) (2024)
- [SALT: A Flexible Semi-Automatic Labeling Tool for General LiDAR Point Clouds with Cross-Scene Adaptability and 4D Consistency](https://mlsanity.com/paper/2503.23980/) (2025)
- [TrackOcc: Camera-based 4D Panoptic Occupancy Tracking](https://mlsanity.com/paper/2503.08471/) (2025)
- [Radar Tracker: Moving Instance Tracking in Sparse and Noisy Radar Point Clouds](https://mlsanity.com/paper/2507.03441/) (2025)
- [ReScene4D: Temporally Consistent Semantic Instance Segmentation of Evolving Indoor 3D Scenes](https://mlsanity.com/paper/2601.11508/) (2026)
- [MCDS-VSS: Moving Camera Dynamic Scene Video Semantic Segmentation by Filtering with Self-Supervised Geometry and Motion](https://mlsanity.com/paper/2405.19921/) (2024)
- [D-PLS: Decoupled Semantic Segmentation for 4D-Panoptic-LiDAR-Segmentation](https://mlsanity.com/paper/2501.15870/) (2025)
- [4DSegStreamer: Streaming 4D Panoptic Segmentation via Dual Threads](https://mlsanity.com/paper/2510.17664/) (2025)
- [Canonical Space Representation for 4D Panoptic Segmentation of Articulated Objects](https://mlsanity.com/paper/2511.05356/) (2025)
- [Training-Free Global Geometric Association for 4D LiDAR Panoptic Segmentation](https://mlsanity.com/paper/2512.18991/) (2025)
- [Bootstrapping a 4D LiDAR Annotation Tool from Video Foundation Models](https://mlsanity.com/paper/2608.25418/) (2026)

## Abstract (arXiv)

In this paper, we develop rotation-equivariant neural networks for 4D panoptic segmentation. 4D panoptic segmentation is a benchmark task for autonomous driving that requires recognizing semantic classes and object instances on the road based on LiDAR scans, as well as assigning temporally consistent IDs to instances across time. We observe that the driving scenario is symmetric to rotations on the ground plane. Therefore, rotation-equivariance could provide better generalization and more robust feature learning. Specifically, we review the object instance clustering strategies and restate the centerness-based approach and the offset-based approach as the prediction of invariant scalar fields and equivariant vector fields. Other sub-tasks are also unified from this perspective, and different invariant and equivariant layers are designed to facilitate their predictions. Through evaluation on the standard 4D panoptic segmentation benchmark of SemanticKITTI, we show that our equivariant models achieve higher accuracy with lower computational costs compared to their non-equivariant counterparts. Moreover, our method sets the new state-of-the-art performance and achieves 1st place on the SemanticKITTI 4D Panoptic Segmentation leaderboard.