Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Discrete & Computational Geometry
Stability of persistence diagrams
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Vines and vineyards by updating persistence in linear time
Proceedings of the twenty-second annual symposium on Computational geometry
A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Analysis of scalar fields over point cloud data
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
Technical Section: Computing smooth approximations of scalar functions with constraints
Computers and Graphics
Topology- and error-driven extension of scalar functions from surfaces to volumes
ACM Transactions on Graphics (TOG)
Technical Section: Shape approximation by differential properties of scalar functions
Computers and Graphics
Optimal reconstruction might be hard
Proceedings of the twenty-sixth annual symposium on Computational geometry
Lipschitz unimodal and isotonic regression on paths and trees
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
wFEM heat kernel: Discretization and applications to shape analysis and retrieval
Computer Aided Geometric Design
Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming
SMI 2013: Steepest descent paths on simplicial meshes of arbitrary dimensions
Computers and Graphics
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We continue the study of topological persistence [5] by investigating 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 functions f on a 2-manifold such ε-simplification exists, and we give an algorithm to construct them in the piecewise linear case.