Reconstruction of n-dimensional convex bodies from surface tensors

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• 作者：Astrid Kousholt ^{kousholt@math.au.dk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：52A20 ; 44A60 ; 60D05
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：83
• 期：Complete
• 页码：115-144
• 全文大小：1063 K

文摘

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.