Local digital algorithms based on n×⋯×n configuration counts are commonly used within science for estimating intrinsic volumes from binary images. This paper investigates multigrid convergence of such algorithms. It is shown that local algorithms for intrinsic volumes other than volume are not multigrid convergent on the class of convex polytopes. In fact, counter examples are plenty. Also on the class of r-regular sets, counter examples to multigrid convergence are constructed for the surface area and the integrated mean curvature. Finally, a multigrid convergent local algorithm in 2D for the Euler characteristic of convex particles with a lower bound on the interior angles is suggested.
|Publisher||Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University|
|Number of pages||40|
|Publication status||Published - 2013|
|Series||CSGB Research Reports|