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- Herbert Edelsbrunner
- EATCS Monographs on Theoretical Computer Science
- 1987

We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental… (More)

- Herbert Edelsbrunner, Ernst P. Mücke
- ACM Trans. Graph.
- 1992

Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the “shape” of the set. For that purpose, this article introduces the formal notion of the family of α-shapes of a finite point set in R<supscrpt>3</supscrpt>. Each shape is a… (More)

- David Cohen-Steiner, Herbert Edelsbrunner, John Harer
- Discrete & Computational Geometry
- 2005

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… (More)

- Herbert Edelsbrunner, David G. Kirkpatrick, Raimund Seidel
- IEEE Trans. Information Theory
- 1983

A generalization of the convex hull of a finite set of points in Akl and Toussaint [ 11, for instance, discuss the relevance the plane is introduced and analyzed. This generalization leads to a family of straight-line graphs, “o-shapes,” which seem to capture the intuitive of the convex hull problem to pattern recognition. By notions of “fine shape” and… (More)

- Herbert Edelsbrunner, Nimish R. Shah
- Int. J. Comput. Geometry Appl.
- 1994

Given a subspace<inline-equation><f><blkbd>X⊆R</blkbd><sup>d</sup></f></inline-equation> and a finite set <inline-equation><f>S⊆<blkbd>R</blkbd><sup>d</sup></f></inline-equation>, we introduce the Delaunay simplicial complex, <inline-equation><f><sc>D</sc><inf><blkbd>X</blkbd></inf></f></inline-equation>, restricted by… (More)

- Herbert Edelsbrunner, Nimish R. Shah
- Algorithmica
- 1992

A set ofn weighted points in general position in ℝ d defines a unique regular triangulation. This paper proves that if the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation. If, in addition, the points are added in a random sequence and the history of the flips is used for locating the next… (More)

- Herbert Edelsbrunner
- Discrete & Computational Geometry
- 1993

Efficient algorithms are described for computing topological,combinatorial, and metric properties of the union of finitely many ballsin <inline-equation><f><blkbd>R</blkbd><sup>d</sup></f></inline-equation>. These algorithms are based on a simplicial complexdual to a certain decomposition of the union of balls, and on shortinclusion-exclusion formulas… (More)

- J Liang, H Edelsbrunner, C Woodward
- Protein science : a publication of the Protein…
- 1998

Identification and size characterization of surface pockets and occluded cavities are initial steps in protein structure-based ligand design. A new program, CAST, for automatically locating and measuring protein pockets and cavities, is based on precise computational geometry methods, including alpha shape and discrete flow theory. CAST identifies and… (More)