Algorithms for Graphics and Imag
Algorithms for Graphics and Imag
Digital Planar Segment Based Polyhedrization for Surface Area Estimation
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Topological Equivalence between a 3D Object and the Reconstruction of Its Digital Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of surface area and surface area measure of three-dimensional sets from digitizations
Image and Vision Computing
Surface area estimation of digitized 3D objects using weighted local configurations
Image and Vision Computing
Multigrid convergence and surface area estimation
Proceedings of the 11th international conference on Theoretical foundations of computer vision
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Local digital algorithms based on n脳驴脳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. On the other hand, for convex particles in 2D with a lower bound on the interior angles, a multigrid convergent local algorithm for the Euler characteristic is constructed. Also on the class of r-regular sets, counter examples to multigrid convergence are constructed for the surface area and the integrated mean curvature.