Reconstruction of n-dimensional convex bodies from surface tensors |
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Institution: | Department of Mathematics, Aarhus University, Ny Munkegade 118, Aarhus, Denmark |
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Abstract: | In this paper, we derive uniqueness and stability results for surface tensors. Further, we develop two algorithms that reconstruct shape of n-dimensional convex bodies. One algorithm requires knowledge of a finite number of surface tensors, whereas the other algorithm is based on noisy measurements of a finite number of harmonic intrinsic volumes. The derived stability results ensure consistency of the two algorithms. Examples that illustrate the feasibility of the algorithms are presented. |
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Keywords: | Convex body Surface tensor Harmonic intrinsic volume Uniqueness Stability Reconstruction algorithm |
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