2016/10/13 by Anne Marie Svane, Eva B. Vedel Jensen, Svane, Anne Marie +1
Computer Science · Mathematics · #28A75 (Secondary) #53C65 (Primary) #60D05 #Classical Analysis and ODEs (math.CA) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1610.04488
openalex publication_date 2016/10/13 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Motivated by applications in local stereology, a new rotational Crofton\nformula is derived for Minkowski tensors. For sets of positive reach, the\nformula shows how rotational averages of intrinsically defined Minkowski\ntensors on sections passing through the origin are related to the geometry of\nthe sectioned set. In particular, for Minkowski tensors of order j-1 on\nj-dimensional linear subspaces, we derive an explicit formula for the\nrotational average involving hypergeometric functions. Sectioning with lines\nand hyperplanes through the origin is considered in detail. We also study the\ncase where the sections are not restricted to pass through the origin. For sets\nof positive reach, we here obtain a Crofton formula for the integral mean of\nintrinsically defined Minkowski tensors on j-dimensional affine subspaces.\n