Offset filtration

The offset filtration is a growing sequence of metric balls used to detect the size and scale of topological features of a data set. The offset filtration commonly arises in persistent homology and the field of topological data analysis. Utilizing a union of balls to approximate the shape of geometric objects was first suggested by Frosini in 1992 in the context of submanifolds of Euclidean space. The construction was independently explored by Robins in 1998, and expanded to considering the collection of offsets indexed over a series of increasing scale parameters, in order to observe the stability of topological features with respect to attractors. Homological persistence as introduced in these papers by Frosini and Robins was subsequently formalized by Edelsbrunner et al. in their seminal 2002 paper Topological Persistence and Simplification. Since then, the offset filtration has become a primary example in the study of computational topology and data analysis.

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