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.

Keywords: Convex body, surface tensor, harmonic intrinsic volume, uniqueness, stability, reconstruction algorithm