CubicalRipser
Fast persistent homology for 1D time series, 2D images, and 3D/4D volumes.
Authors: Takeki Sudo, Kazushi Ahara (Meiji University), Shizuo Kaji (Kyoto University)
CubicalRipser adapts Ripser by Ulrich Bauer to cubical complexes. It provides C++ command-line programs and a Python package, with V- and T-constructions, coefficients in F₂, creator/destroyer locations, optional representative cycles, zigzag persistence of time-varying binary masks, and PyTorch integration.
Read the manual · Try in Google Colab · Release notes
Quickstart
Python 3.9 or later:
python -m pip install -U numpy cripser
import numpy as np
import cripser
# A low-valued ring surrounding a high-valued center.
image = np.ones((7, 7), dtype=np.float64)
image[1:6, 1:6] = 0.0
image[2:5, 2:5] = 1.0
ph = cripser.compute_ph(image, filtration="V", maxdim=1)
print(ph[:, :3]) # homology dimension, birth, death
Use filtration="T" for T-construction. Results also include creator/destroyer
coordinates; essential classes have death=np.inf. See the
Python API and output semantics.
For the CLI, build the binaries, then run from the repository root.
The input below is a hollow sphere from cripser.datasets:
python -c "import numpy as np, cripser; np.save('sphere.npy', cripser.datasets.sphere((32, 32, 32)))"
./build/cubicalripser --maxdim 2 --output out.csv sphere.npy
./build/tcubicalripser --maxdim 2 --output out_t.csv sphere.npy
Documentation
| Task | Guide |
|---|---|
| Install Python or build from source | Installation |
| Compute PH in Python or from the terminal | Python API · CLI |
| Load images, volumes, and slice stacks | Input and output |
| Understand V/T constructions and coordinates | Constructions and output semantics |
| Extract and visualize cycles | Representative cycles |
| Track features through videos and time-lapse masks | Zigzag persistence |
| Plot diagrams or create feature arrays | Plotting and vectorization |
| Use topology in differentiable workflows | PyTorch and distances |
| Test changes and check performance | Development and validation |
| Compare other implementations | Related software |
More tutorials and application examples are listed in the manual.
Citation
If you use this software in research, please cite:
@misc{2005.12692,
author = {Shizuo Kaji and Takeki Sudo and Kazushi Ahara},
title = {Cubical Ripser: Software for computing persistent homology of image and volume data},
year = {2020},
eprint = {arXiv:2005.12692}
}
License
Distributed under the GNU Lesser General Public License v3.0 or later. See LICENSE.
1 maintainer
Metadata
1 maintainer
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