PyEMD is a Python wrapper for Ofir Pele and Michael Werman's implementation of the Earth Mover's Distance that allows it to be used with NumPy. If you use this code, please cite the papers listed at the end of this document.
To install the latest release:
pip install pyemd
Before opening an issue related to installation, please try to install PyEMD in a fresh, empty Python 3 virtual environment and check that the problem persists.
>>> from pyemd import emd
>>> import numpy as np
>>> first_histogram = np.array([0.0, 1.0])
>>> second_histogram = np.array([5.0, 3.0])
>>> distance_matrix = np.array([[0.0, 0.5],
... [0.5, 0.0]])
>>> emd(first_histogram, second_histogram, distance_matrix)
3.5
You can also get the associated minimum-cost flow:
>>> from pyemd import emd_with_flow
>>> emd_with_flow(first_histogram, second_histogram, distance_matrix)
(3.5, [[0.0, 0.0], [0.0, 1.0]])
emd(first_histogram, second_histogram, distance_matrix)
first_histogram
: A 1-dimensional numpy array of typenp.float64
, of length N.second_histogram
: A 1-dimensional numpy array of typenp.float64
, of length N.distance_matrix
: A 2-dimensional array of typenp.float64
, of size at least N \times N. This defines the underlying metric, or ground distance, by giving the pairwise distances between the histogram bins. It must represent a metric; there is no warning if it doesn't.
The arguments to emd_with_flow
are the same.
distance_matrix
is assumed to represent a metric; there is no check to ensure that this is true. See the documentation inpyemd/lib/emd_hat.hpp
for more information.- The flow matrix does not contain the flows to/from the extra mass bin.
- The histograms and distance matrix must be numpy arrays of type
np.float64
. The original C++ template function can accept any numerical C++ type, but this wrapper only instantiates the template withdouble
(Cython convertsnp.float64
todouble
). If there's demand, I can add support for other types.
To help develop PyEMD, fork the project on GitHub and install the requirements
with pip
.
The Makefile
defines some tasks to help with development:
default
: compile the Cython code into C++ and build the C++ into a Python extension, using thesetup.py
build commandbuild
: same as default, but using thecython
commandclean
: remove the build directory and the compiled C++ extensiontest
: run unit tests withpy.test
Tests for different Python environments can be run by installing tox
with
pip install tox
and running the tox
command.
- All credit for the actual algorithm and implementation goes to Ofir Pele and Michael Werman. See the relevant paper.
- Thanks to the Cython devlopers for making this kind of wrapper relatively easy to write.
Ofir Pele and Michael Werman, "A linear time histogram metric for improved SIFT matching," in Computer Vision - ECCV 2008, Marseille, France, 2008, pp. 495-508.
@INPROCEEDINGS{pele2008,
title={A linear time histogram metric for improved sift matching},
author={Pele, Ofir and Werman, Michael},
booktitle={Computer Vision--ECCV 2008},
pages={495--508},
year={2008},
month={October},
publisher={Springer}
}
Ofir Pele and Michael Werman, "Fast and robust earth mover's distances," in Proc. 2009 IEEE 12th Int. Conf. on Computer Vision, Kyoto, Japan, 2009, pp. 460-467.
@INPROCEEDINGS{pele2009,
title={Fast and robust earth mover's distances},
author={Pele, Ofir and Werman, Michael},
booktitle={2009 IEEE 12th International Conference on Computer Vision},
pages={460--467},
year={2009},
month={September},
organization={IEEE}
}