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

LiDAR point clouds are fundamental to various applications, yet the extreme sparsity of high-precision geometric details hinders efficient context modeling, thereby limiting the compression speed and performance of existing methods. To address this challenge, we propose a compact representation for efficient predictive lossless coding. Our framework comprises two lightweight modules. First, the Geometry Re-Densification Module iteratively densifies encoded sparse geometry, extracts features at a dense scale, and then sparsifies the features for predictive coding. This module avoids costly computation on highly sparse details while maintaining a lightweight prediction head. Second, the Cross-scale Feature Propagation Module leverages occupancy cues from multiple resolution levels to guide hierarchical feature propagation, enabling information sharing across scales and reducing redundant feature extraction. Additionally, we introduce an integer-only inference pipeline to enable bit-exact cross-platform consistency, which avoids the entropy-coding collapse observed in existing neural compression methods and further accelerates coding. Experiments demonstrate competitive compression performance at real-time speed. Code will be released upon acceptance. Code is available at https://github.com/pengpeng-yu/FastPCC.

Efficient point cloud geometry compression (PCGC) is essential for 3D sensing applications such as autonomous driving and digital twins. Hybrid methods combine the generalization of learned models with the adaptability of Implicit Neural Representations (INRs), but existing schemes often use complex architectures, rigid update strategies, and post-training weight compression, limiting adaptation efficiency and increasing bitstream overhead. This paper proposes Hybrid-PCGC, which formulates hybrid compression as a joint geometry-and-model bitrate allocation problem and optimizes instance-specific weight offsets as rate-constrained transmitted variables. It separates dataset-agnostic prior modeling from instance-specific adaptation through four components: a Frozen General Module (FGM), a Dual Trainable Adaptive Module (DTAM), an Adaptive Scope Controller (ASC), and a Supervised Offset Compression Module (SOCM). FGM captures global geometric regularities, while the parameter-efficient DTAM adapts to individual point clouds. ASC selects the update scope based on coding difficulty, and SOCM jointly optimizes and compresses weight offsets through differentiable entropy supervision during training. Experiments show that Hybrid-PCGC balances fidelity and bitrate, reducing bitrate by 13.96% and 16.33% over G-PCC on lossless and lossy benchmarks, respectively, and saving up to 12.33% bitrate over the state-of-the-art hybrid method on challenging dense point clouds.

Three-dimensional reconstruction from unorganized point clouds remains a challenging problem in computer vision, geometric modeling, and computer-aided design. While neural implicit methods achieve impressive reconstruction accuracy, geometry is typically encoded in latent representations that limit interpretability and reuse within engineering workflows. We present NeuSOGA3D (Neuro-Symbolic Observation-Guided Geometric Abstraction in 3D), a hybrid framework that combines learned perceptual priors inherited from NeuSOGA with explicit symbolic geometric reasoning. The method projects point clouds onto principal orthographic planes, constructs symbolic implicit spline representations from the resulting observations, and fuses them through shape-preserving constructive solid geometry operations to generate a coarse visual hull. Additional geometric detail is recovered through cross-sectional decomposition and volumetric reconstruction using Partial Shape-Preserving Splines. Unlike conventional neural implicit approaches, NeuSOGA3D progressively transforms observations into explicit symbolic entities, including control polygons, implicit spline fields, cross-sections, and volumetric lofts. Experiments on all forty categories of the ModelNet40 benchmark demonstrate the ability of the framework to recover structurally meaningful and CAD-compatible geometric representations from diverse point-cloud observations. The results highlight the potential of combining learned perception with symbolic geometric reasoning for explainable geometric intelligence.