Fourier Decomposition for Explicit Representation of 3D Point Cloud Attributes

While 3D point clouds are widely used in 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 serve as more expressive 3D representations encompassing both color and geometry. While existing methods handle color and geometry 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 colored 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 our 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. We validate our colored point cloud encoding approach on classification, segmentation, and style transfer tasks, achieving state-of-the-art results on the DensePoint dataset.