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.

alt tag

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.

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.

License

Released under the MIT License. See LICENSE.

Release files for pycirclemedianfilter 1.0.0

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Source distribution (sdist)

Source distribution for pycirclemedianfilter 1.0.0
File	Size	Uploaded
pycirclemedianfilter-1.0.0.tar.gz	12.6 kB	May 11, 2026	Details

Built distributions (wheels)

Table of built distributions (wheels) for pycirclemedianfilter 1.0.0
File	Interpreter	ABI	Platform	Reset
pycirclemedianfilter-1.0.0-cp313-cp313-win_amd64.whl 83.9 kB May 11, 2026	CPython 3.13	CPython 3.13	Windows x86-64	Details
pycirclemedianfilter-1.0.0-cp313-cp313-win32.whl 73.3 kB May 11, 2026	CPython 3.13	CPython 3.13	Windows x86-32	Details
pycirclemedianfilter-1.0.0-cp313-cp313-musllinux_1_2_x86_64.whl 2.2 MB May 11, 2026	CPython 3.13	CPython 3.13	Linux musl 1.2+ x86-64	Details
pycirclemedianfilter-1.0.0-cp313-cp313-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl 1.2 MB May 11, 2026	CPython 3.13	CPython 3.13	Linux glibc 2.24+ x86-64, Linux glibc 2.28+ x86-64	Details
pycirclemedianfilter-1.0.0-cp313-cp313-macosx_11_0_arm64.whl 223.0 kB May 11, 2026	CPython 3.13	CPython 3.13	macOS 11.0+ ARM64	Details
pycirclemedianfilter-1.0.0-cp312-cp312-win_amd64.whl 83.8 kB May 11, 2026	CPython 3.12	CPython 3.12	Windows x86-64	Details
pycirclemedianfilter-1.0.0-cp312-cp312-win32.whl 73.3 kB May 11, 2026	CPython 3.12	CPython 3.12	Windows x86-32	Details
pycirclemedianfilter-1.0.0-cp312-cp312-musllinux_1_2_x86_64.whl 2.2 MB May 11, 2026	CPython 3.12	CPython 3.12	Linux musl 1.2+ x86-64	Details
pycirclemedianfilter-1.0.0-cp312-cp312-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl 1.2 MB May 11, 2026	CPython 3.12	CPython 3.12	Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64	Details
pycirclemedianfilter-1.0.0-cp312-cp312-macosx_11_0_arm64.whl 222.8 kB May 11, 2026	CPython 3.12	CPython 3.12	macOS 11.0+ ARM64	Details
pycirclemedianfilter-1.0.0-cp311-cp311-win_amd64.whl 82.3 kB May 11, 2026	CPython 3.11	CPython 3.11	Windows x86-64	Details
pycirclemedianfilter-1.0.0-cp311-cp311-win32.whl 72.5 kB May 11, 2026	CPython 3.11	CPython 3.11	Windows x86-32	Details
pycirclemedianfilter-1.0.0-cp311-cp311-musllinux_1_2_x86_64.whl 2.2 MB May 11, 2026	CPython 3.11	CPython 3.11	Linux musl 1.2+ x86-64	Details
pycirclemedianfilter-1.0.0-cp311-cp311-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl 1.2 MB May 11, 2026	CPython 3.11	CPython 3.11	Linux glibc 2.24+ x86-64, Linux glibc 2.28+ x86-64	Details
pycirclemedianfilter-1.0.0-cp311-cp311-macosx_11_0_arm64.whl 218.5 kB May 11, 2026	CPython 3.11	CPython 3.11	macOS 11.0+ ARM64	Details
pycirclemedianfilter-1.0.0-cp310-cp310-win_amd64.whl 81.8 kB May 11, 2026	CPython 3.10	CPython 3.10	Windows x86-64	Details
pycirclemedianfilter-1.0.0-cp310-cp310-win32.whl 71.5 kB May 11, 2026	CPython 3.10	CPython 3.10	Windows x86-32	Details
pycirclemedianfilter-1.0.0-cp310-cp310-musllinux_1_2_x86_64.whl 2.2 MB May 11, 2026	CPython 3.10	CPython 3.10	Linux musl 1.2+ x86-64	Details
pycirclemedianfilter-1.0.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 1.3 MB May 11, 2026	CPython 3.10	CPython 3.10	Linux glibc 2.17+ x86-64	Details
pycirclemedianfilter-1.0.0-cp310-cp310-macosx_11_0_arm64.whl 218.2 kB May 11, 2026	CPython 3.10	CPython 3.10	macOS 11.0+ ARM64	Details
pycirclemedianfilter-1.0.0-cp39-cp39-win_amd64.whl 81.8 kB May 11, 2026	CPython 3.9	CPython 3.9	Windows x86-64	Details
pycirclemedianfilter-1.0.0-cp39-cp39-win32.whl 71.6 kB May 11, 2026	CPython 3.9	CPython 3.9	Windows x86-32	Details
pycirclemedianfilter-1.0.0-cp39-cp39-musllinux_1_2_x86_64.whl 2.2 MB May 11, 2026	CPython 3.9	CPython 3.9	Linux musl 1.2+ x86-64	Details
pycirclemedianfilter-1.0.0-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 1.3 MB May 11, 2026	CPython 3.9	CPython 3.9	Linux glibc 2.17+ x86-64	Details
pycirclemedianfilter-1.0.0-cp39-cp39-macosx_11_0_arm64.whl 218.5 kB May 11, 2026	CPython 3.9	CPython 3.9	macOS 11.0+ ARM64	Details

Total release size: 19.0 MB

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Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Publishing platform: GitHub Actions
Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Release files / pycirclemedianfilter-1.0.0-cp311-cp311-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl

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Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Release files / pycirclemedianfilter-1.0.0-cp311-cp311-macosx_11_0_arm64.whl

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Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Release files / pycirclemedianfilter-1.0.0-cp310-cp310-win_amd64.whl

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Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Publishing platform: GitHub Actions
Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Publishing platform: GitHub Actions
Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Release files / pycirclemedianfilter-1.0.0-cp310-cp310-macosx_11_0_arm64.whl

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Publishing platform: GitHub Actions
Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Release files / pycirclemedianfilter-1.0.0-cp39-cp39-win_amd64.whl

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Uploaded via	`twine/6.1.0 CPython/3.13.12`

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Publishing platform: GitHub Actions
Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Release files / pycirclemedianfilter-1.0.0-cp39-cp39-win32.whl

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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.12`

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Publishing platform: GitHub Actions
Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Release files / pycirclemedianfilter-1.0.0-cp39-cp39-musllinux_1_2_x86_64.whl

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Upload date	May 11, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.12`

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Publishing platform: GitHub Actions
Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Publishing logs: github.com/mstorath/CircleMedianFilter/actions/runs/25659016165/attempts/1

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Release files / pycirclemedianfilter-1.0.0-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl

Download URL	pycirclemedianfilter-1.0.0-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl
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Upload date	May 11, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.12`

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Publishing platform: GitHub Actions
Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Publishing configuration: github.com/mstorath/CircleMedianFilter/blob/64858b9344114a505a782f9d59877286914c1152/.github/workflows/build_wheels.yml
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Release files / pycirclemedianfilter-1.0.0-cp39-cp39-macosx_11_0_arm64.whl

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Upload date	May 11, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.12`

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Publishing platform: GitHub Actions
Publishing repository: github.com/mstorath/CircleMedianFilter
Publishing commit: github.com/mstorath/CircleMedianFilter/tree/64858b9344114a505a782f9d59877286914c1152

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Publishing configuration: github.com/mstorath/CircleMedianFilter/blob/64858b9344114a505a782f9d59877286914c1152/.github/workflows/build_wheels.yml
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Artifact

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SHA-256 checksum: 7024d7fb844e7892cff0d57e82dd69869905bca79a75976b00f5590f2997cbcf Verifying attestations

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1.0.0 This release

May 11, 2026 26 release files

0.1.7

May 7, 2026 26 release files

0.1.6

Feb 18, 2025 45 release files

0.1.5

Feb 18, 2025 30 release files

pycirclemedianfilter 1.0.0

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

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Release files / pycirclemedianfilter-1.0.0.tar.gz

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Release files / pycirclemedianfilter-1.0.0-cp313-cp313-win_amd64.whl

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