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With the increased use of virtual and augmented reality applications, the importance of point cloud data rises. High-quality capturing of point clouds is still expensive and thus, the need for point cloud super-resolution or point cloud upsampling techniques emerges. In this paper, we propose an interpolation scheme for color upsampling of three-dimensional color point clouds. As a point cloud represents an object's surface in three-dimensional space, we first conduct a local transform of the surface into a two-dimensional plane. Secondly, we propose to apply a novel Frequency-Selective Mesh-to-Mesh Resampling (FSMMR) technique for the interpolation of the points in 2D. FSMMR generates a model of weighted superpositions of basis functions on scattered points. This model is then evaluated for the final points in order to increase the resolution of the original point cloud. Evaluation shows that our approach outperforms common interpolation schemes. Visual comparisons of the jaguar point cloud underlines the quality of our upsampling results. The high performance of FSMMR holds for various sampling densities of the input point cloud.