https://github.com/mstorath/mumfordshah2d
Algorithms for edge preserving smoothing based on the Mumford-Shah model
https://github.com/mstorath/mumfordshah2d
admm deconvolution edge-detection edge-preserving image-processing image-reconstruction image-segmentation image-smoothing java matlab mumford-shah-model mumfordshahmodel python regularization rust
Last synced: 18 days ago
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Algorithms for edge preserving smoothing based on the Mumford-Shah model
- Host: GitHub
- URL: https://github.com/mstorath/mumfordshah2d
- Owner: mstorath
- Created: 2020-02-06T11:10:18.000Z (over 6 years ago)
- Default Branch: master
- Last Pushed: 2026-05-08T06:56:13.000Z (26 days ago)
- Last Synced: 2026-05-08T08:22:35.654Z (26 days ago)
- Topics: admm, deconvolution, edge-detection, edge-preserving, image-processing, image-reconstruction, image-segmentation, image-smoothing, java, matlab, mumford-shah-model, mumfordshahmodel, python, regularization, rust
- Language: Jupyter Notebook
- Homepage:
- Size: 14.1 MB
- Stars: 0
- Watchers: 1
- Forks: 4
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE
- Citation: CITATION.cff
Awesome Lists containing this project
README
# MumfordShah2D — Edge-preserving image restoration via the Mumford-Shah model
[](https://pypi.org/project/mumfordshah2d/)
[](https://pypi.org/project/mumfordshah2d/)
[](LICENSE)
[](https://github.com/mstorath/MumfordShah2D/actions/workflows/ci.yml)
[](#matlab)
Edge-preserving image restoration via the Mumford-Shah model — denoising, deconvolution, and inpainting of vector-valued images with linear complexity in the number of channels and no a-priori label discretisation.
## Paper
> K. Hohm, M. Storath, A. Weinmann.
> [*An algorithmic framework for Mumford-Shah regularization of inverse problems in imaging.*](http://bigwww.epfl.ch/publications/hohm1501.pdf)
> Inverse Problems 31(11), 115011, 2015.
## Quickstart
### Python (Rust core)
```bash
pip install mumfordshah2d
```
```python
import numpy as np
from mumfordshah2d import min_l2_mum_2d
# noisy grayscale image
f = np.random.randn(64, 64) + your_image
u = min_l2_mum_2d(f, gamma=0.5, alpha=1.0)
```
The Python package wraps a Rust extension built with [PyO3](https://pyo3.rs)
and [maturin](https://maturin.rs); algorithm crate lives under `src/`,
demos under [`demos_python/`](demos_python/).
See [`README_PYTHON.md`](README_PYTHON.md) for the full Python API,
including soft / hard thresholding utilities and prox handles.
### MATLAB
The original MATLAB / Java reference implementation is in this same repository:
1. Run `setPath.m` to add the necessary folders to the MATLAB path.
2. For best performance, increase Java heap space in the MATLAB preferences (MATLAB → General → Java Heap Memory).
3. Run a demo from the `Demos/` folder.
## Application examples
### Edge-preserving smoothing of vector-valued images
- Supports smoothing of vector-valued images (e.g. multispectral, feature images)
- Linear complexity in the number of channels
- No discretisation of colour space required
(See hero image above for the salt-and-pepper denoising case.)
### Regularization for deconvolution
### Inpainting
## How to cite
If you use this software, please cite the paper above. GitHub's "Cite this repository" button on the repo page reads the `version` and `date-released` fields from [`CITATION.cff`](CITATION.cff) and renders BibTeX/APA.
## See also
Sibling projects from the same research program on variational methods for signal and image processing:
- [Pottslab](https://github.com/mstorath/Pottslab) — multilabel image segmentation via the Potts / piecewise-constant Mumford-Shah model
- [L1TV](https://github.com/mstorath/L1TV) — exact L1-TV regularisation of real- or circle-valued signals
- [CSSD](https://github.com/mstorath/CSSD) — cubic smoothing splines for signals with discontinuities
- [CircleMedianFilter](https://github.com/mstorath/CircleMedianFilter) — fast median filtering for phase or orientation data
- [DCEBE](https://github.com/mstorath/DCEBE) — bolus arrival time estimation for DCE-MRI signals
## License
Released under the MIT License. See [LICENSE](LICENSE).
---
### Project history
The Python / Rust port of this codebase was generated from the original MATLAB / Java reference by a Claude coding agent in 2026.
See [`PORTED_BY.md`](PORTED_BY.md) for full attribution and the porting plan.