Permutation-Invariant Polar Harmonic Pooling for Point-based Neural Networks


Jaspreet Singh Maan (University of Lincoln), Grzegorz Cielniak (University of Lincoln)
The 35th British Machine Vision Conference
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Abstract

Point-based learning methods have recently gained significant attention for point cloud data analysis. These neural networks typically consist of a permutation-equivariant backbone network for feature extraction, a symmetric global pooling operation for feature aggregation, and a permutation-invariant classification or regression head. Most of the prior work has focused on improving the equivariant backbone while the global pooling operation crucial for effective feature summarization has remained relatively underexplored. In this paper, we introduce Polar Harmonic Pooling (PHP), a novel symmetric global pooling method that leverages polar harmonic transforms to aggregate point cloud features. Unlike traditional pooling methods that rely on simple statistical measures, PHP captures global frequency patterns across the point set. This approach yields a more expressive and compact representation by encoding both spatial structure and frequency-domain characteristics in polar coordinates. We evaluate PHP on both classification and regression tasks. Experimental results show that PHP enhances accuracy, reduces the number of parameters in the invariant classification or regression head, and helps reducing overfitting when compared to standard statistical pooling methods.

Citation

@inproceedings{Maan_2025_BMVC,
author    = {Jaspreet Singh Maan and Grzegorz Cielniak},
title     = {Permutation-Invariant Polar Harmonic Pooling for Point-based Neural Networks},
booktitle = {36th British Machine Vision Conference 2025, {BMVC} 2025, Sheffield, UK, November 24-27, 2025},
publisher = {BMVA},
year      = {2025},
url       = {https://bmva-archive.org.uk/bmvc/2025/assets/papers/Paper_381/paper.pdf}
}


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