Nerve Theorem on a Positive Reach set
Kim, Jisu ; Shin, Jaehyeok ; Rinaldo, Alessandro ; Wasserman, Larry
arXiv, Tome 2019 (2019) no. 0, / Harvested from
We provide sufficient conditions under which any non-empty intersection of finitely many Euclidean balls intersected with a subset of $\mathbb{R}^d$ of positive reach are contractible. Our result allows for an immediate application of the nerve theorem to the problem of recovering the homology of a set based on point cloud data.
Publié le : 2019-03-16
Classification:  Mathematics - Algebraic Topology,  Computer Science - Computational Geometry 
@article{1903.06955,
     author = {Kim, Jisu and Shin, Jaehyeok and Rinaldo, Alessandro and Wasserman, Larry},
     title = {Nerve Theorem on a Positive Reach set},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1903.06955}
}

Kim, Jisu; Shin, Jaehyeok; Rinaldo, Alessandro; Wasserman, Larry. Nerve Theorem on a Positive Reach set. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1903.06955/