pycmf 0.1.0
A Circle Median Filter package for Python
Requires Python: >=3.6

# Circle median filter toolbox (CMF)
 
This toolbox contains a fast algorithm for median filtering of signals and images with values on the unit circle, for example phase or orientation data.
The (arc distance) median filter for an image y with values on the unit circle is given by 

<img src="docs/eqArcDistanceMedian.png" width="40%">

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

The code is a reference implementation (in C++ with Matlab wrappers) of the algorithms described in the paper:

Martin Storath, Andreas Weinmann.
[Fast median filtering for phase or orientation data.](https://doi.org/10.1109/TPAMI.2017.2692779)
IEEE Transactions on Pattern Analysis and Machine Intelligence, 	40(3):639-652, 2018  ([preprint](https://hci.iwr.uni-heidelberg.de/sites/default/files/profiles/mstorath/files/storath2017fast.pdf))

See also [![View Circle Median Filter on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://de.mathworks.com/matlabcentral/fileexchange/62509-circle-median-filter)

### Example 


![alt tag](https://hci.iwr.uni-heidelberg.de/sites/default/files/publications/teaserimages/1908951751/mediancircularrevision_teaser_small.png)

*Left:* A circle-valued image, i.e. every pixel takes its value on the unit circle (or in angular representation a value in (-pi, pi]). The values are visualized as hue component in the HSV color space.
*Right:* Effect of the circle-median filter using a filter mask of size 7 × 7. 

### Runtime comparison

The time complexity w.r.t. the size of the filter mask is
- linear for non-quantized data
- constant for quantized data

<img src="docs/runtime.png" width="80%">

### Applications

- Smoothing of phase data, e.g. interferometric SAR images
   ![alt tag](docs/InSAR.png)
- Smoothing of orientation data, e.g. wind directions

   <img src="docs/windDirections.png" width="60%">
   
- Smoothing of vector fields in polar coordinates, e.g. optical flow images

### Contents
- demos:     some demos, self explanatory (implemented in Matlab)
- auxiliary: some useful helper functions (implemented in Matlab)
- filters:   the fast algorithms for median filtering of circle valued data 
(implemented in C++ with Matlab wrappers)

### Installation and usage

- From Matlab: Run CMF_install.m in the Matlab console and follow the demos 
- From C++: Compile CMF_library.cpp. The relevant functions are medfiltCirc2D and medfiltCirc2DQuant. Their usage is described as comment in the CMF_library.cpp file.

## References
### How to cite
- M. Storath, A. Weinmann. [Fast median filtering for phase or orientation data.](https://doi.org/10.1109/TPAMI.2017.2692779) IEEE Transactions on Pattern Analysis and Machine Intelligence, 40(3):639-652, 2018
### 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
- 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
- B. Guo, J. Wen, Y. Han. Deep Material Recognition in Light-Fields via Disentanglement of Spatial and Angular Information. ECCV 2020