MumfordShah2D

May 11, 2026 · View on GitHub

PyPI Python License: MIT CI 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.

Mumford-Shah denoising example

Paper

K. Hohm, M. Storath, A. Weinmann. An algorithmic framework for Mumford-Shah regularization of inverse problems in imaging. Inverse Problems 31(11), 115011, 2015.

Quickstart

Python (Rust core)

pip install mumfordshah2d

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 and maturin; algorithm crate lives under src/, demos under demos_python/. See 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

Deconvolution

Inpainting

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 and renders BibTeX/APA.

See also

Sibling projects from the same research program on variational methods for signal and image processing:

  • Pottslab — multilabel image segmentation via the Potts / piecewise-constant Mumford-Shah model
  • L1TV — exact L1-TV regularisation of real- or circle-valued signals
  • CSSD — cubic smoothing splines for signals with discontinuities
  • CircleMedianFilter — fast median filtering for phase or orientation data
  • DCEBE — bolus arrival time estimation for DCE-MRI signals

License

Released under the MIT License. See 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 for full attribution and the porting plan.