Towards persistence-based reconstruction in euclidean spaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Translated Poisson Mixture Model for Stratification Learning
International Journal of Computer Vision
Persistent homology for kernels, images, and cokernels
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proximity of persistence modules and their diagrams
Proceedings of the twenty-fifth annual symposium on Computational geometry
Reconstructing shapes with guarantees by unions of convex sets
Proceedings of the twenty-sixth annual symposium on Computational geometry
Local homology transfer and stratification learning
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We study the reconstruction of a stratified space from a possibly noisy point sample. Specifically, we use the vineyard of the distance function restricted to a 1-parameter family of neighborhoods of a point to assess the local homology of the stratified space at that point. We prove the correctness of this assessment under the assumption of a sufficiently dense sample. We also give an algorithm that constructs the vineyard and makes the local assessment in time at most cubic in the size of the Delaunay triangulation of the point sample.