topapprox
Authors: Matias de Jong van Lier, Junyan Chu, Sebastían Elías Graiff Zurita, Shizuo Kaji
topapprox is a Python package for persistent-homology-based filtering of scalar signals on:
- 1D, 2D, and 3D arrays
- graphs with faces
Low-persistence filtering removes topological features that are small relative to a chosen threshold epsilon.
In practice:
- Build the persistence diagram of the input signal.
- Identify features whose persistence is smaller than
epsilon. - Modify the signal so those low-persistence features disappear, while the more significant ones remain.
This makes the filter useful for denoising and simplification: small oscillations, shallow basins, and weak cycles are removed, while large-scale structure is preserved. For array signals, the filtered output remains within epsilon in the L^inf norm of the original input.
Installation
From PyPI:
pip install topapprox
From source:
python -m pip install -e ".[dev]"
Quick Start
import numpy as np
import topapprox as ta
from topapprox.persistence import get_PD_gwf
img = np.array([[0, 5, 3], [5, 6, 4], [2, 5, 1]], dtype=float)
image_filter = ta.ImageFilter(img, method="python")
filtered_h0 = image_filter.low_pers_filter(1.5)
dual_filter = ta.ImageFilter(img, dual=True, method="python")
filtered_h1 = dual_filter.low_pers_filter(1.5)
faces = [[0, 1, 2, 3]]
holes = [[0, 1, 2, 3]]
signal = np.array([0.0, 1.0, 0.5, 0.2])
graph_filter = ta.GraphFilter(method="python")
graph_filter.compute_gwf(F=faces, H=holes, signal=signal)
pd0, pd1 = graph_filter.get_diagram()
persistence_filter = ta.PersistenceFilter().load_signal(img)
filtered_01 = persistence_filter.low_pers_filter(1.5, iteration_order="01", method="python")
pd0_fn, pd1_fn = get_PD_gwf(faces, holes, signal, method="python")
Documentation & Examples
- Interactive Tutorial
- BHT Basin Visualization
- Reproducing Paper Examples
- Notebook/API migration memo
- Original paper on arXiv
Development
Run the full test suite:
python -m pytest -q
Build distributions locally:
python -m build --wheel --sdist
Binary wheels are built with cibuildwheel, and the native extension is compiled through scikit-build-core + CMake.
Citation
If you use this package in your work, please cite:
Matias de Jong van Lier, Sebastían Elías Graiff Zurita, Shizuo Kaji. Topological filtering of a signal over a network (2024). arXiv:2408.14109
@article{vanlier2024topological,
title={Topological filtering of a signal over a network},
author={de Jong van Lier, Matias and Graiff Zurita, Sebastían Elías and Kaji, Shizuo},
journal={arXiv preprint arXiv:2408.14109},
year={2024}
}
Migration Notes
The refactor intentionally simplified the public surface and build system. If you are adapting older notebooks, see docs/migration.md.
Metadata
Release files for topapprox 0.2.1
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Source distribution (sdist)
| File | Size | Uploaded | |
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| topapprox-0.2.1.tar.gz | 3.3 MB | Details |
Built distributions (wheels)
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twine/6.1.0 CPython/3.13.12
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Transparency logRelease files / topapprox-0.2.1-cp310-cp310-manylinux_2_17_i686.manylinux2014_i686.whl
| Download URL | topapprox-0.2.1-cp310-cp310-manylinux_2_17_i686.manylinux2014_i686.whl |
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| Size | 146.8 kB |
| Tags | CPython 3.10 Linux glibc 2.17+ x86-32 |
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SHA-256 checksum How to use checksums |
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twine/6.1.0 CPython/3.13.12
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Transparency logRelease files / topapprox-0.2.1-cp310-cp310-macosx_11_0_arm64.whl
| Download URL | topapprox-0.2.1-cp310-cp310-macosx_11_0_arm64.whl |
|---|---|
| Size | 101.7 kB |
| Tags | CPython 3.10 macOS 11.0+ ARM64 |
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SHA-256 checksum How to use checksums |
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BLAKE2b-256 checksum How to use checksums |
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twine/6.1.0 CPython/3.13.12
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