Voronoi-Based Estimation of Minkowski Tensors from Finite Point Samples

TY - JOUR

T1 - Voronoi-Based Estimation of Minkowski Tensors from Finite Point Samples

AU - Hug, Daniel

AU - Kiderlen, Markus

AU - Svane, Anne Marie

PY - 2017/4/1

Y1 - 2017/4/1

N2 - Intrinsic volumes and Minkowski tensors have been used to describe the geometry of real world objects. This paper presents an estimator that allows approximation of these quantities from digital images. It is based on a generalized Steiner formula for Minkowski tensors of sets of positive reach. When the resolution goes to infinity, the estimator converges to the true value if the underlying object is a set of positive reach. The underlying algorithm is based on a simple expression in terms of the cells of a Voronoi decomposition associated with the image.

AB - Intrinsic volumes and Minkowski tensors have been used to describe the geometry of real world objects. This paper presents an estimator that allows approximation of these quantities from digital images. It is based on a generalized Steiner formula for Minkowski tensors of sets of positive reach. When the resolution goes to infinity, the estimator converges to the true value if the underlying object is a set of positive reach. The underlying algorithm is based on a simple expression in terms of the cells of a Voronoi decomposition associated with the image.

KW - Digital algorithm

KW - Digitization

KW - Minkowski tensor

KW - Set of positive reach

UR - https://www.scopus.com/pages/publications/85007614175

U2 - 10.1007/s00454-016-9851-x

DO - 10.1007/s00454-016-9851-x

M3 - Journal article

SN - 0179-5376

VL - 57

SP - 545

EP - 570

JO - Discrete & Computational Geometry

JF - Discrete & Computational Geometry

IS - 3

ER -