# Self-Supervised Robust Scene Flow Estimation via the Alignment of Probability Density Functions

arXiv: https://arxiv.org/abs/2203.12193 · HTML: https://mlsanity.com/paper/2203.12193/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 60 references that are in the map.
- First posted on arXiv 23 Mar 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [FLOT: Scene Flow on Point Clouds Guided by Optimal Transport](https://mlsanity.com/paper/2007.11142/) (2020)
- [RAFT-3D: Scene Flow using Rigid-Motion Embeddings](https://mlsanity.com/paper/2012.00726/) (2020)
- [HPLFlowNet: Hierarchical Permutohedral Lattice FlowNet for Scene Flow Estimation on Large-scale Point Clouds](https://mlsanity.com/paper/1906.05332/) (2019)
- [Just Go with the Flow: Self-Supervised Scene Flow Estimation](https://mlsanity.com/paper/1912.00497/) (2019)
- [DeepGMR: Learning Latent Gaussian Mixture Models for Registration](https://mlsanity.com/paper/2008.09088/) (2020)
- [PV-RAFT: Point-Voxel Correlation Fields for Scene Flow Estimation of Point Clouds](https://mlsanity.com/paper/2012.00987/) (2020)
- [FlowStep3D: Model Unrolling for Self-Supervised Scene Flow Estimation](https://mlsanity.com/paper/2011.10147/) (2020)
- [Weakly Supervised Learning of Rigid 3D Scene Flow](https://mlsanity.com/paper/2102.08945/) (2021)
- [Scene Flow from Point Clouds with or without Learning](https://mlsanity.com/paper/2011.00320/) (2020)
- [Self-Supervised Learning of Non-Rigid Residual Flow and Ego-Motion](https://mlsanity.com/paper/2009.10467/) (2020)
- [Self-Point-Flow: Self-Supervised Scene Flow Estimation from Point Clouds with Optimal Transport and Random Walk](https://mlsanity.com/paper/2105.08248/) (2021)
- [Learning Scene Dynamics from Point Cloud Sequences](https://mlsanity.com/paper/2111.08755/) (2021)
- [Adversarial Self-Supervised Scene Flow Estimation](https://mlsanity.com/paper/2011.00551/) (2020)

## Built on by (most cited first, 7 of 7)

- [SCOOP: Self-Supervised Correspondence and Optimization-Based Scene Flow](https://mlsanity.com/paper/2211.14020/) (2022)
- [Self-Supervised 3D Scene Flow Estimation Guided by Superpoints](https://mlsanity.com/paper/2305.02528/) (2023)
- [The Conditional Cauchy-Schwarz Divergence with Applications to Time-Series Data and Sequential Decision Making](https://mlsanity.com/paper/2301.08970/) (2023)
- [Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformations](https://mlsanity.com/paper/2209.02152/) (2022)
- [Self-Supervised 3D Scene Flow Estimation and Motion Prediction using Local Rigidity Prior](https://mlsanity.com/paper/2310.11284/) (2023)
- [Weakly and Self-Supervised Class-Agnostic Motion Prediction for Autonomous Driving](https://mlsanity.com/paper/2509.13116/) (2025)
- [Active Velocity Estimation using Light Curtains via Self-Supervised Multi-Armed Bandits](https://mlsanity.com/paper/2302.12597/) (2023)

## Abstract (arXiv)

In this paper, we present a new self-supervised scene flow estimation approach for a pair of consecutive point clouds. The key idea of our approach is to represent discrete point clouds as continuous probability density functions using Gaussian mixture models. Scene flow estimation is therefore converted into the problem of recovering motion from the alignment of probability density functions, which we achieve using a closed-form expression of the classic Cauchy-Schwarz divergence. Unlike existing nearest-neighbor-based approaches that use hard pairwise correspondences, our proposed approach establishes soft and implicit point correspondences between point clouds and generates more robust and accurate scene flow in the presence of missing correspondences and outliers. Comprehensive experiments show that our method makes noticeable gains over the Chamfer Distance and the Earth Mover's Distance in real-world environments and achieves state-of-the-art performance among self-supervised learning methods on FlyingThings3D and KITTI, even outperforming some supervised methods with ground truth annotations.