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

2026-09-26

AI Summary

This study addresses the prohibitive computational and storage overheads associated with implicit representations of large-scale point clouds by proposing a unified framework that integrates implicit fields, hierarchical frequency-domain compression, and conditional high-frequency prediction. The proposed method maps point clouds into an implicit geometric field and constructs a smooth Fourier pyramid to enable hierarchical frequency-domain compression, while leveraging conditional high-frequency prediction to recover local details. Point clouds are subsequently reconstructed via isosurface extraction, effectively balancing global structural fidelity with local geometric accuracy. Experimental results demonstrate that, on complex boundary data comprising over eight million points, this approach achieves superior compression ratios compared to existing state-of-the-art methods while maintaining comparable reconstruction quality.

Abstract

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.

Problem

• Large-scale point clouds
• Implicit geometric representations
• Compression
• Computational cost
• Memory cost

Innovation

• Implicit Geometric Representation
• Hierarchical Frequency-Domain Compression
• Point Cloud Compression
• Fourier Pyramid
• Conditional High-Frequency Prediction