Point Clouds in the Frequency Domain: Color in Amplitude, Geometry in Phase

Point clouds are widely used in vision applications, and colored point clouds, a more expressive 3D representation that encompasses both color and geometry, are becoming the norm in scanned and reconstructed data. Yet, a fundamental limitation persists: existing methods have largely been developed for point clouds with coordinates alone and simply append RGB values to each point as additional channels, leaving color and geometry entangled in the learned features. To address this, we pioneer the analysis of the amplitude and phase of colored point clouds under 3D Fourier decomposition. By reading color and geometry out of the amplitude and phase alone and by swapping the two components between point clouds, we find that color resides in the amplitude and geometry in the phase. Building on this finding, we propose an input scheme that takes amplitude and phase as inputs, so that color and geometry are learned independently. With this simple idea, our models perform favorably against recent methods on classification and segmentation of colored point clouds.