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

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.