#### Filter Results:

#### Publication Year

1981

2016

#### Publication Type

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

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)

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)

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)

We present algorithms for constructing a hierarchy of increasingly coarse Morse-Smale complexes that decompose a piecewise linear 2-manifold. While these complexes are defined only in the smooth category, we extend the construction to the piecewise linear category by ensuring structural integrity and simulating differentiability. We then simplify… (More)

ACKNOWLEDGMENT The authors express their appreciation for numerous constructive suggestions, which led to improvements on various phases of the manuscript, to Dr. A high performance multiple data rate burst modem for satellite packet communication, " EASCON Conference Record, Nov. 198 1. A microprocessor-based PSK modem for packet transmission over… (More)

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)