Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysis [CVPR 2026]

About

This repository contains the official implementation of Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysis (in press CVPR 2026) and reproducible experiments from the corresponding paper. arXiv

Dependencies

This implementation was tested with Ubuntu 18.04, Python 3.11 with CUDA 12.4. Refer to environment.yml

• PyTorch==2.4.1
• PyTorch3D
• wandb

Dataset Configuration

• ModelNet40: Download modelnet40_normal_resampled.
• ShapeNetPart: Download shapenetpart_hdf5_2048.
• S3DIS: Download s3dis-compressed, which is a preprocessed version provided by Pointcept/Pointcept.

Training

ModelNet40 Classification

# ECKConv
python train_modelnet_cls.py --cfg se3_conv_arch_3 --lr 1e-4 --use_noisy --use_scheduler --use_smoothing
# ECKConv with SO(3) Augmentation
python train_modelnet_cls.py --cfg se3_conv_arch_3 --lr 1e-4 --use_noisy --use_scheduler --use_smoothing --use_rotate
# ECKConv-mini
python train_modelnet_cls.py --cfg se3_conv_arch_mini --lr 1e-4 --use_noisy --use_scheduler --use_smoothing
# ECKConv-mini with SO(3) Augmentation
python train_modelnet_cls.py --cfg se3_conv_arch_mini --lr 1e-4 --use_noisy --use_scheduler --use_smoothing --use_rotate
# ECKConv-Normal
python train_modelnet_cls.py --cfg se3_conv_arch_3 --lr 1e-4 --use_noisy --use_scheduler --use_smoothing  --use_normal
# ECKConv-Normal with SO(3) Augmentation
python train_modelnet_cls.py --cfg se3_conv_arch_3 --lr 1e-4 --use_noisy --use_scheduler --use_smoothing --use_normal --use_rotate

ModelNet40 Pose Registration

# ECKConv + DCP-v2
python train_modelnet_reg.py --cfg se3conv_reg_0 --lr 1e-4 --epochs 50 --use_scheduler

ShapeNetPart Segmentation

# ECKConv 
python train_shapenetpart.py --cfg shapenet_deconv_0 --epochs 250 --lr 1e-4 --use_noisy --use_scheduler --use_smoothing
# ECKConv with SO(3) Augmentation
python train_shapenetpart.py --cfg shapenet_deconv_0 --epochs 250 --lr 1e-4 --use_noisy --use_scheduler --use_smoothing --use_rotate

S3DIS Segmentation

# ECKConv-Normal
python train_s3dis.py --cfg s3dis_deconv_no_color_1 --batchsize 8 --epochs 80 --use_noisy --use_labelweight--log_every 600

Evaluation

To reproduce the results, download the zipped weight file (Google Drive), unzip it in this repository, and use below commands.

ModelNet40 Classification

# ECKConv
python test_modelnet_cls.py --weight weight/modelnet/se3_no_normal_align.pth
# ECKConv with SO(3) Augmentation
python test_modelnet_cls.py --weight weight/modelnet/se3_no_normal_so3.pth
# ECKConv-mini
python test_modelnet_cls.py --weight weight/modelnet/se3_mini_align.pth
# ECKConv-mini with SO(3) Augmentation
python test_modelnet_cls.py --weight weight/modelnet/se3_mini_so3.pth
# ECKConv-Normal
python test_modelnet_cls.py --weight weight/modelnet/se3_normal_align.pth
# ECKConv-Normal with SO(3) Augmentation
python test_modelnet_cls.py --weight weight/modelnet/se3_normal_so3.pth

ModelNet40 Pose Registration

# ECKConv + DCP-v2
python test_modelnet_reg.py --weight weight/modelnet_reg/se3_no_normal.pth

ShapeNetPart Segmentation

# ECKConv 
python test_shapenetpart.py --weight weight/shapenetpart/se3_no_normal_align.pth
# ECKConv with SO(3) Augmentation
python test_shapenetpart.py --weight weight/shapenetpart/se3_no_normal_so3.pth

S3DIS Segmentation

# ECKConv-Normal
python test_s3dis.py --weight weight/s3dis/se3conv_best.pth

Acknowledgements

The implementations and dataset preparations in this repository are based on jykim2958/CSEConv, yanx27/Pointnet_Pointnet2_pytorch, WangYueFt/dcp, apple/ml-kpconvx, antao97/PointCloudDatasets, and Pointcept/Pointcept.

Citation

@misc{kim2026learning
      title={Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysis}, 
      author={Jaein Kim and Hee Bin Yoo and Dong-Sig Han and Byoung-Tak Zhang},
      year={2026},
      eprint={2603.17538},
      archivePrefix={arXiv},
      primaryClass={cs.CV},
      url={https://arxiv.org/abs/2603.17538}, 
}