Reconstruction of $n$-dimensional convex bodies from surface tensors

TL;DR

This paper presents new algorithms for reconstructing n-dimensional convex bodies using surface tensors, with proven uniqueness and stability, and demonstrates their effectiveness through examples.

Contribution

It introduces two algorithms for convex body reconstruction from surface tensors and harmonic intrinsic volumes, with stability guarantees and practical illustrations.

Findings

Algorithms successfully reconstruct convex bodies from surface tensors.

Stability results ensure reliable reconstruction despite measurement noise.

Feasibility demonstrated through illustrative examples.

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.