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Markus Kiderlen

Reconstruction of convex bodies from surface tensors

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We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise variables.
Original languageEnglish
PublisherCentre for Stochastic Geometry and advanced Bioimaging, Aarhus University
Number of pages29
Publication statusPublished - 2015
SeriesCSGB Research Reports
Number10

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