Python Empirical Mode Decomposition on Image
One of the packages I intend long term maintain and support is Python implementation of Empirical Mode Decomposition (EMD) called PyEMD. I will skip introduction of the method as it has been explained in few other posts [1, 2, 3, ...]. This blog entry is more about announcement of new feature which also means new version.
PyEMD version 0.2 is out. This means that PyEMD now supports 2D data (image) decomposition. Other visible improvements include documentation and more thorough testing both of code and data cases. Installation instructions are provided on the project's webpage.
I am more than happy to include other improvements or suggestions. The next big step will be support for 3D and multi dimensional data. Please get in touch if you feel that there is something missing.
Image decomposition is based on the simple extremum definition: a point that is above (max) or below (min) surrounding. Behind the hood this is done using SciPy's ndim maximum_filter. These are then connected using SmoothBivariateSpline. Stopping criteria can be chosen to be either based on the number of sifting operations or threshold values for mean and standard deviations.
Below is included exemplary decomposition, with the top image being input and the following two are the outputs. Exact formula with which the image was generated is $sin(4\pi \cdot x) \cdot \left( cos(8\pi y + 8\pi x) + 3\right) + \left(5x + 2y - 0.4 \right) y + 2$. Python code generating this example is in provided in documentation in Examples/EMD2D.