Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Introduction to Algorithms
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Persistence barcodes for shapes
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Inequalities for the curvature of curves and surfaces
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Stability and homotopy of a subset of the medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Inequalities for the curvature of curves and surfaces
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
A Topological Approach to Simplification of Three-Dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Vines and vineyards by updating persistence in linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Persistence-sensitive simplification functions on 2-manifolds
Proceedings of the twenty-second annual symposium on Computational geometry
A sampling theory for compact sets in Euclidean space
Proceedings of the twenty-second annual symposium on Computational geometry
Provably good sampling and meshing of Lipschitz surfaces
Proceedings of the twenty-second annual symposium on Computational geometry
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
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Geodesic Delaunay triangulation and witness complex in the plane
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Towards persistence-based reconstruction in euclidean spaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Approximating the pathway axis and the persistence diagram of a collection of balls in 3-space
Proceedings of the twenty-fourth annual symposium on Computational geometry
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Multidimensional Size Functions for Shape Comparison
Journal of Mathematical Imaging and Vision
Analysis of scalar fields over point cloud data
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
Proximity of persistence modules and their diagrams
Proceedings of the twenty-fifth annual symposium on Computational geometry
Isotopic reconstruction of surfaces with boundaries
SGP '09 Proceedings of the Symposium on Geometry Processing
Gromov-Hausdorff stable signatures for shapes using persistence
SGP '09 Proceedings of the Symposium on Geometry Processing
Topological inference via meshing
Proceedings of the twenty-sixth annual symposium on Computational geometry
International Journal of Computer Vision
The Geometric Stability of Voronoi Diagrams with Respect to Small Changes of the Sites
Proceedings of the twenty-seventh annual symposium on Computational geometry
A new algorithm for computing the 2-dimensional matching distance between size functions
Pattern Recognition Letters
Shape reconstruction from unorganized set of points
ICIAR'10 Proceedings of the 7th international conference on Image Analysis and Recognition - Volume Part I
Linear-size approximations to the vietoris-rips filtration
Proceedings of the twenty-eighth annual symposium on Computational geometry
Persistence-Based Clustering in Riemannian Manifolds
Journal of the ACM (JACM)
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The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result to estimating the homology of sets in a metric space and to comparing and classifying geometric shapes.