A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Surface Area Estimation of Digitized 3D Objects Using Local Computations
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
The Algorithm Design Manual
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
Measuring intrinsic volumes in digital 3d images
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Surface area estimation of digitized 3D objects using quasi-Monte Carlo methods
Pattern Recognition
On Multigrid Convergence of Local Algorithms for Intrinsic Volumes
Journal of Mathematical Imaging and Vision
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A local method for estimating surface area and surface area measure of three-dimensional objects from discrete binary images is presented. A weight is assigned to each 2x2x2 configuration of voxels and the total surface area of an object is given by summation of the local area contributions. The method is based on an exact asymptotic result that holds for increasing resolution of the digitization. It states that the number of occurrences of a 2x 2x2 configuration is asymptotically proportional to an integral of its ''h-function'' with respect to the surface area measure of the object. We find explicit representations for these h-functions. Analyzing them in detail, we determine weights that lead to an asymptotic worst case error for surface area estimation of less than 4%. We show that this worst case error is the best possible. Exploiting the local nature of the asymptotic result, we also establish two parametric estimators for the surface area measure. The latter allow to quantify anisotropy of the object under consideration. Simulation studies illustrate the validity of the estimation procedure also for finite, but sufficiently high resolution.