Stability of Persistence Diagrams Export

@article{citeulike:3197375, abstract = {Abstract\ \ 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.}, author = {Cohen-Steiner, David and Edelsbrunner, Herbert and Harer, John}, citeulike-article-id = {3197375}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=1229140}, citeulike-linkout-1 = {http://dx.doi.org/10.1007/s00454-006-1276-5}, citeulike-linkout-2 = {http://www.springerlink.com/content/f51r061k4x3x6u54}, day = {6}, doi = {10.1007/s00454-006-1276-5}, journal = {Discrete and Computational Geometry}, keywords = {3d\_reconstruction, noise\_reduction, point\_cloud, surface\_fitting, thesis}, month = {January}, number = {1}, pages = {103--120}, posted-at = {2008-11-27 13:03:23}, priority = {4}, title = {Stability of Persistence Diagrams}, url = {http://dx.doi.org/10.1007/s00454-006-1276-5}, volume = {37}, year = {2007} }

TY - JOUR ID - citeulike:3197375 L3 - citeulike-article-id:3197375 N2 - Abstract  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. IS - 1 JF - Discrete and Computational Geometry EP - 120 TI - Stability of Persistence Diagrams VL - 37 SP - 103 KW - 3d_reconstruction KW - noise_reduction KW - point_cloud KW - surface_fitting KW - thesis AU - Cohen-Steiner, David AU - Edelsbrunner, Herbert AU - Harer, John PY - 2007/01/06/ UR - http://dx.doi.org/10.1007/s00454-006-1276-5 ER -