Fourier Decomposition for Explicit Representation of 3D Point Cloud Attributes

2025-03-13

AI Summary

To address the coupled color-geometry representation and limited local receptive fields in colored point clouds, this paper proposes a novel 3D Fourier-based spectral encoding method. It introduces 3D Fourier Transform to point cloud processing for the first time, explicitly decoupling amplitude (dominant for color semantics) and phase (dominant for geometric structure) in the frequency domain—enabling attribute-separated modeling and global cross-point feature aggregation. We further design an amplitude-driven data augmentation strategy and an end-to-end architecture supporting both classification and style transfer. Evaluated on the DensePoint dataset, our method achieves state-of-the-art performance on both point cloud classification and style transfer tasks, significantly outperforming existing approaches. Key contributions include: (1) the first application of 3D Fourier analysis to colored point clouds; (2) explicit spectral disentanglement of color and geometry; (3) global feature learning via frequency-domain aggregation; and (4) a unified framework enabling joint classification and style transfer with enhanced generalization.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

While 3D point clouds are widely utilized across various vision applications, their irregular and sparse nature make them challenging to handle. In response, numerous encoding approaches have been proposed to capture the rich semantic information of point clouds. Yet, a critical limitation persists: a lack of consideration for colored point clouds which are more capable 3D representations as they contain diverse attributes: color and geometry. While existing methods handle these attributes separately on a per-point basis, this leads to a limited receptive field and restricted ability to capture relationships across multiple points. To address this, we pioneer a point cloud encoding methodology that leverages 3D Fourier decomposition to disentangle color and geometric features while extending the receptive field through spectral-domain operations. Our analysis confirms that this encoding approach effectively separates feature components, where the amplitude uniquely captures color attributes and the phase encodes geometric structure, thereby enabling independent learning and utilization of both attributes. Furthermore, the spectral-domain properties of these components naturally aggregate local features while considering multiple points' information. We validate our point cloud encoding approach on point cloud classification and style transfer tasks, achieving state-of-the-art results on the DensePoint dataset with improvements via a proposed amplitude-based data augmentation strategy.

Problem

• Handling irregular and sparse 3D point clouds
• Separating color and geometric features in point clouds
• Extending receptive field for multi-point relationships

Innovation

• 3D Fourier decomposition for feature separation
• Spectral-domain operations extend receptive field
• Amplitude and phase encode color and geometry