Overview
This is the project page of flooder, an easy-to-use Python package for constructing a lightweight simplicial complex (i.e., the FLood complex) on top of (low-dimensional) Euclidean point cloud data and subsequent persistent homology1 (PH) computation. Algorithmically, flooder is designed to take full advantage of state-of-the-art GPU computing frameworks (via PyTorch) to enable computation of a filtered simplicial complex on millions of points in seconds. Based on the Flood complex, we use the awesome gudhi library for PH computation.
Illustration
Below is an illustrative animation on how the (filtered) Flood complex is built (on a noisy sample of a figure-eight shape in 2D), starting from a collection of points and a Delaunay triangulation of a small subset of landmarks (in yellow). In short, a simplex of the Delaunay triangulation is added to the Flood complex at time \(t\geq 0\), if it is fully covered by balls of radius \(t\), centered at all data points.
Runtime teaser
Below you find a runtime comparison of computing zero-, one-, and two-dimensional Flood and Alpha PH on 1M points in 3D (using a NVIDIA H100 NVL GPU). The data used in this comparison is a synthetic (3D) swiss cheese created by uniformly drawing points in the unit cube and introducing a certain number of voids. Note that on point clouds of this size (in fact, even at much lower scale), computing Vietoris-Rips PH is intractable (beyond 0-dimensional features). The table lists runtime in seconds (for creating the filtered Flood and Alpha complexes and subsequent PH computation).
| Complex | Runtime (in s) |
|---|---|
Alpha complex (via gudhi.AlphaComplex) |
141.8 \(\pm\) 1.5 |
| Flood complex (via flooder) | 1.4 \(\pm\) 0.3 |
Please see our examples folder in the flooder GitHub repository to run your own runtime comparison.
Caution
flooder is still under active development and it's usage API might change significantly over the next months.