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Stability of Persistence Diagrams
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
Proximity of persistence modules and their diagrams
TLDR
This paper presents new stability results that do not suffer from the restrictions of existing stability results, and makes it possible to compare the persistence diagrams of functions defined over different spaces, thus enabling a variety of new applications of the concept of persistence.
Variational tetrahedral meshing
TLDR
A novel Delaunay-based variational approach to isotropic tetrahedral meshing is presented, which minimize a simple mesh-dependent energy through global updates of both vertex positions and connectivity and generates well-shaped tetrahedra.
Stability of Persistence Diagrams
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
Anisotropic polygonal remeshing
TLDR
A novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or man-made geometry, and provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.
Variational shape approximation
TLDR
A novel and versatile framework for geometric approximation of surfaces is presented, casting shape approximation as a variational geometric partitioning problem and using the concept of geometric proxies to drive the distortion error down through repeated clustering of faces into best-fitting regions.
Restricted delaunay triangulations and normal cycle
TLDR
A definition of the curvature tensor for polyhedral surfaces is derived in a very simple and new formula that yields an efficient and reliable curvature estimation algorithm.
Vines and vineyards by updating persistence in linear time
TLDR
The main result of this paper is an algorithm that maintains the pairing in worst-case linear time per transposition in the ordering and uses the algorithm to compute 1-parameter families of diagrams which are applied to the study of protein folding trajectories.
Geometric Inference for Probability Measures
TLDR
Replacing compact subsets by measures, a notion of distance function to a probability distribution in ℝd is introduced and it is shown that it is possible to reconstruct offsets of sampled shapes with topological guarantees even in the presence of outliers.
Lipschitz Functions Have Lp-Stable Persistence
TLDR
Two stability results for Lipschitz functions on triangulable, compact metric spaces are proved and applications of both to problems in systems biology are considered.
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