Abstract
Minkowski tensors contain information about shape and orientation of the underlying convex body. We make this precise by showing that reconstructing a centered ellipse in two-dimensional Euclidean space from its rank-2 surface tensor is a well-posed inverse problem. It turns out that this result can be restated equivalently with other geometric tomography data derived from the support function of the ellipse, such as the first three non-trivial Fourier coefficients. We present explicit reconstruction algorithms for all three types of input. The relevance of these findings is illustrated in an application to stationary particle processes. We define and discuss two shape ellipses, each containing information about the mean shape and orientation of the typical particle.
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This research was partially supported by Centre for Stochastic Geometry and Advanced Bioimaging, funded by the Villum Foundation.
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Eriksen, R., Kiderlen, M. Reconstructing Planar Ellipses from Translation-Invariant Minkowski Tensors of Rank Two. Discrete Comput Geom 69, 1095–1120 (2023). https://doi.org/10.1007/s00454-022-00470-0
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DOI: https://doi.org/10.1007/s00454-022-00470-0