Reconstruction of n-dimensional convex bodies from surface tensors

2016/06/27 by Kousholt, Astrid
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1606.08240

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.

Related

• Surface tensor estimation from linear sections
• Reconstruction of convex bodies from moments
• Reconstruction of Centrally Symmetrical Convex Bodies by Projection Curvature Radii
• An algorithm to reconstruct convex polyhedra from their face normals and areas
• Reconstruction of Convex Bodies from Projection Curvature Radius Function