Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Reconstruction curves with sharp corners
Proceedings of the sixteenth annual symposium on Computational geometry
The flow complex: a data structure for geometric modeling
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
A geometric convection approach of 3-D reconstruction
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Stability and Finiteness Properties of Medial Axis and Skeleton
Journal of Dynamical and Control Systems
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Spectral surface reconstruction from noisy point clouds
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Stability of persistence diagrams
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Graphical Models
Topology guaranteeing manifold reconstruction using distance function to noisy data
Proceedings of the twenty-second annual symposium on Computational geometry
Analysis of the spatial distribution of galaxies by multiscale methods
EURASIP Journal on Applied Signal Processing
Provably good sampling and meshing of Lipschitz surfaces
Proceedings of the twenty-second annual symposium on Computational geometry
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Weak witnesses for Delaunay triangulations of submanifolds
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Shape smoothing using double offsets
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Manifold reconstruction in arbitrary dimensions using witness complexes
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Reconstruction using witness complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Complexity of Delaunay triangulation for points on lower-dimensional polyhedra
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Geodesic Delaunay triangulation and witness complex in the plane
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees
Computational Geometry: Theory and Applications
Towards persistence-based reconstruction in euclidean spaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Persistent homology for kernels, images, and cokernels
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Normal cone approximation and offset shape isotopy
Computational Geometry: Theory and Applications
Manifold homotopy via the flow complex
SGP '09 Proceedings of the Symposium on Geometry Processing
Isotopic reconstruction of surfaces with boundaries
SGP '09 Proceedings of the Symposium on Geometry Processing
Stability of curvature measures
SGP '09 Proceedings of the Symposium on Geometry Processing
Road network reconstruction for organizing paths
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The Geometric Stability of Voronoi Diagrams with Respect to Small Changes of the Sites
Proceedings of the twenty-seventh annual symposium on Computational geometry
Reconstructing 3D compact sets
Computational Geometry: Theory and Applications
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We introduce a parameterized notion of feature size that interpolates between the minimum of the local feature size, and the recently introduced weak feature size. Based on this notion of feature size, we propose sampling conditions that apply to noisy samplings of general compact sets in euclidean space. These conditions are sufficient to ensure the topological correctness of a reconstruction given by an offset of the sampling. Our approach also yields new stability results for medial axes, critical points and critical values of distance functions.