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arXiv · 2512.17382

Delaunay-Rips filtration: a study and an algorithm

Mattéo Clémot·Julie Digne·Julien Tierny
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Abstract

The Delaunay-Rips filtration is a lighter and faster alternative to the well-known Rips filtration for low-dimensional Euclidean point clouds. Despite these advantages, it has seldom been studied. In this paper, we aim to bridge this gap by providing a thorough theoretical and empirical analysis of this construction. From a theoretical perspective, we show how the persistence diagrams associated with the Delaunay-Rips filtration approximate those obtained with the Rips filtration. Additionally, we describe the instabilities of the Delaunay-Rips persistence diagrams when the input point cloud is perturbed. Finally, we introduce an algorithm that computes persistence diagrams of Delaunay-Rips filtrations in any dimension. We show that our method is faster and has a lower memory footprint than traditional approaches in low dimensions. Our C++ implementation, which comes with Python bindings, is available at https://github.com/MClemot/GeoPH.

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Mattéo Clémot, Julie Digne, Julien Tierny. 2025-12-19. Delaunay-Rips filtration: a study and an algorithm. https://arxiv.org/abs/2512.17382

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