# Hierarchical Frequency-Domain Compression of Implicit Geometric Representations for Large-Scale Point Clouds

arXiv: https://arxiv.org/abs/2609.32789 · HTML: https://mlsanity.com/paper/2609.32789/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [OctSqueeze: Octree-Structured Entropy Model for LiDAR Compression](https://mlsanity.com/paper/2005.07178/) (2020)
- [Sparse Tensor-based Multiscale Representation for Point Cloud Geometry Compression](https://mlsanity.com/paper/2111.10633/) (2021)
- [VoxelContext-Net: An Octree based Framework for Point Cloud Compression](https://mlsanity.com/paper/2105.02158/) (2021)
- [Improved Implicit Neural Representation with Fourier Reparameterized Training](https://mlsanity.com/paper/2401.07402/) (2024)
- [Deep Implicit Volume Compression](https://mlsanity.com/paper/2005.08877/) (2020)
- [TINC: Tree-structured Implicit Neural Compression](https://mlsanity.com/paper/2211.06689/) (2022)
- [UniPCGC: Towards Practical Point Cloud Geometry Compression via an Efficient Unified Approach](https://mlsanity.com/paper/2503.18541/) (2025)
- [Hierarchical Prior-based Super Resolution for Point Cloud Geometry Compression](https://mlsanity.com/paper/2402.11250/) (2024)
- [Learning Neural Volumetric Field for Point Cloud Geometry Compression](https://mlsanity.com/paper/2212.05589/) (2022)

## Abstract (arXiv)

Large-scale point cloud representations of complex geome tries incur prohibitive computational and memory costs, necessitating compressed implicit representations. To ad dress this, we propose a unified framework comprising im plicit geometric field representation, hierarchical frequency domain compression, and conditional high-frequency predic tion. Specifically, an unordered point cloud is mapped to an implicit field defined within its physical bounding box. A smooth Fourier pyramid is then constructed, where com pact low-frequency components capture the global geometry. Inter-scale high-frequency residuals are encoded to preserve the spatial information required for reconstructing fine geo metric details. To restore the high-frequency information lost during compression, we develop a hierarchical 3D neural net work. The reconstructed implicit field is converted back into a point cloud through isosurface extraction. Experiments on a complex-boundary point cloud with more than eight mil lion points demonstrate that the proposed method achieves a higher compression ratio than existing point cloud compres sion methods while maintaining comparable reconstruction quality.