Numerical Reconstruction of Convex Polytopes from Directional Moments

Abstract : We reconstruct an n-dimensional convex polytope from the knowledge of its directional moments up to a certain order. The directional moments are related to the projection of the polytope's vertices on a particular direction. To extract the vertex coordinates from the moment information we combine established numerical algorithms such as generalized eigenvalue computation and linear interval interpolation. Numerical illustrations are given for the reconstruction of 2-d and 3-d objects.
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Mathieu Collowald, Annie Cuyt, Evelyne Hubert, Wen-Shin Lee, Oliver Salazar Celis. Numerical Reconstruction of Convex Polytopes from Directional Moments. Advances in Computational Mathematics, Springer Verlag, 2015, 41 (6), pp.21. ⟨10.1007/s10444-014-9401-0⟩. ⟨hal-00926357v2⟩

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