CircleMedianFilter

CircleMedianFilter (CMF) — Fast median filtering for phase or orientation data

A fast median filter for signals and images whose values lie on the unit circle (phase, orientation, interferometric SAR, wind directions, optical-flow angles). Linear in filter mask size for non-quantised data, constant for quantised data.

Left: A circle-valued image — every pixel takes its value on the unit circle (or in angular representation a value in (-π, π]), visualised as the hue component in the HSV colour space. Right: Effect of the circle-median filter using a 7 × 7 mask.

The (arc distance) median filter for an image y with values on the unit circle is given by

where d denotes the arc distance length of two angles, and r, t are the horizontal and vertical “radii” of the filter mask.

Paper

M. Storath, A. Weinmann. Fast median filtering for phase or orientation data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 40(3):639–652, 2018. preprint

Quickstart

Python

pip install pycirclemedianfilter

Input arrays are accepted in either C-order or Fortran-order (since v0.1.7 the binding auto-converts as needed). Outputs are Fortran-strided. See demos_python/ for examples.

MATLAB

• Run CMF_install.m in the MATLAB console and follow the demos in demos_matlab/.

C++

• Compile CMF_library.cpp. The relevant functions are medfiltCirc2D and medfiltCirc2DQuant. Their usage is documented as comments in CMF_library.cpp.

Runtime comparison

Time complexity with respect to filter mask size is

• linear for non-quantised data,
• constant for quantised data.

Applications

• Smoothing of phase data, e.g. interferometric SAR images

  

• Smoothing of orientation data, e.g. wind directions

  

• Smoothing of vector fields in polar coordinates, e.g. optical-flow images.

Updates

• 2025/02/18: Added Python bindings for the core C++ filtering code.

Contents

• demos_matlab/ — MATLAB demos
• demos_python/ — Python demos
• auxiliary/ — helper functions (MATLAB)
• filters/ — the fast algorithms for median filtering of circle-valued data (C++ with MATLAB wrappers)

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.

Selected user applications

• S. Quan et al. Derivation of the orientation parameters in built-up areas: with application to model-based decomposition. IEEE Transactions on Geoscience and Remote Sensing, 2018.
• H. Salmane et al. A method for the automated detection of solar radio bursts in dynamic spectra. J. Space Weather Space Clim. 2018.
• B. Guo, J. Wen, Y. Han. Deep material recognition in light-fields via disentanglement of spatial and angular information. ECCV 2020.

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
• MumfordShah2D — edge-preserving image restoration via the Mumford-Shah model
• DCEBE — bolus arrival time estimation for DCE-MRI signals

License

Released under the MIT License. See LICENSE.

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