This paper proposes a new method for reconstruction of star-shaped 3D surfaces from scattered datasets, where such surfaces are considered as signals living in the space of square integrable functions on the unit sphere. We first propose a generalization of the Fourier transform on the sphere. A practical reconstruction method is then presented, which interpolates a spherical signal on an equiangular grid, from non-uniformly sampled dataset representing a 3D point cloud. The experiments show that the proposed interpolation method results in smoother surfaces, and higher reconstruction PSNRs than the nearest neighbor interpolation method.
Alfio Quarteroni, Francesco Regazzoni
Jürg Alexander Schiffmann, Phillip Huwiler, Davide Pradovera