Geometric and Topological Inference

It was written by Jean-Daniel Boissonnat, Frédéric Chazal, and Mariette Yvinec, and published in 2018 by the Cambridge University Press in their Cambridge Texts in Applied Mathematics book series.

A second introductory part concerns material of a more geometric nature, including Delaunay triangulations and Voronoi diagrams, convex polytopes, convex hulls and convex hull algorithms, lower envelopes, alpha shapes and alpha complexes, and witness complexes.

[3] With these preliminaries out of the way, the remaining two sections show how to use these tools for topological inference.

[1][3][4] Although the book is primarily aimed at specialists in these topics, it can also be used to introduce the area to non-specialists, and provides exercises suitable for an advanced course.

[4][2] Reviewer Michael Berg evaluates it as an "excellent book" aimed at a hot topic, inference from large data sets,[1] and both Berg and Mark Hunacek note that it brings a surprising level of real-world applicability to formerly-pure topics in mathematics.