Persistence-sensitive simplification of functions on 2-manifolds

H. Edelsbrunner, D. Morozov, V. Pascucci, in:, ACM, 2006, pp. 127–134.

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Abstract
We continue the study of topological persistence [5] by investigat- ing the problem of simplifying a function f in a way that removes topological noise as determined by its persistence diagram [2]. To state our results, we call a function g an ε-simplification of another function f if ∥f − g∥∞ ≤ ε, and the persistence diagrams of g are the same as those of f except all points within L1-distance at most ε from the diagonal have been removed. We prove that for func- tions f on a 2-manifold such ε-simplification exists, and we give an algorithm to construct them in the piecewise linear case.
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Date Published
2006-06-01
Acknowledgement
Partially supported by NSF under grant CCR-00-86013, by DARPA under grant HR0011-05-1-0007, and by the Lawrence Livermore National Laboratory under grant B543154.
Page
127 - 134
Conference
SCG: Symposium on Computational Geometry
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Edelsbrunner H, Morozov D, Pascucci V. Persistence-sensitive simplification of functions on 2-manifolds. In: ACM; 2006:127-134. doi:10.1145/1137856.1137878
Edelsbrunner, H., Morozov, D., & Pascucci, V. (2006). Persistence-sensitive simplification of functions on 2-manifolds (pp. 127–134). Presented at the SCG: Symposium on Computational Geometry, ACM. https://doi.org/10.1145/1137856.1137878
Edelsbrunner, Herbert, Dmitriy Morozov, and Valerio Pascucci. “Persistence-Sensitive Simplification of Functions on 2-Manifolds,” 127–34. ACM, 2006. https://doi.org/10.1145/1137856.1137878.
H. Edelsbrunner, D. Morozov, and V. Pascucci, “Persistence-sensitive simplification of functions on 2-manifolds,” presented at the SCG: Symposium on Computational Geometry, 2006, pp. 127–134.
Edelsbrunner H, Morozov D, Pascucci V. 2006. Persistence-sensitive simplification of functions on 2-manifolds. SCG: Symposium on Computational Geometry 127–134.
Edelsbrunner, Herbert, et al. Persistence-Sensitive Simplification of Functions on 2-Manifolds. ACM, 2006, pp. 127–34, doi:10.1145/1137856.1137878.

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