Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
The union of balls and its dual shape
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A survey of methods for recovering quadrics in triangle meshes
ACM Computing Surveys (CSUR)
The flow complex: a data structure for geometric modeling
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Estimating differential quantities using polynomial fitting of osculating jets
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
A sampling theory for compact sets in Euclidean space
Proceedings of the twenty-second annual symposium on Computational geometry
Reassembling fractured objects by geometric matching
ACM SIGGRAPH 2006 Papers
Shape smoothing using double offsets
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Robust statistical estimation of curvature on discretized surfaces
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Principal curvatures from the integral invariant viewpoint
Computer Aided Geometric Design
Integral invariants for robust geometry processing
Computer Aided Geometric Design
Generalized Curvatures
Anisotropic smoothing of point sets
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Voronoi-Based extraction of a feature skeleton from noisy triangulated surfaces
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part II
Curvature tensor computation by piecewise surface interpolation
Computer-Aided Design
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We address the problem of curvature estimation from sampled compact sets. The main contribution is a stability result: we show that the Gaussian, mean or anisotropic curvature measures of the offset of a compact set K with positive μ-reach can be estimated by the same curvature measures of the offset of a compact set K' close to K in the Hausdorff sense. We show how these curvature measures can be computed for finite unions of balls. The curvature measures of the offset of a compact set with positive μ-reach can thus be approximated by the curvature measures of the offset of a point-cloud sample.