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Description:

pyefd 1.6.0

PyEFD

An Python/NumPy implementation of a method for approximating a contour with a Fourier series, as described in [1].
Installation
pip install pyefd

Usage
Given a closed contour of a shape, generated by e.g. scikit-image or
OpenCV, this package can fit a
Fourier series approximating the shape of the contour.
General usage examples
This section describes the general usage patterns of pyefd.
from pyefd import elliptic_fourier_descriptors
coeffs = elliptic_fourier_descriptors(contour, order=10)

The coefficients returned are the a_n, b_n, c_n and d_n of the following Fourier series
representation of the shape.
The coefficients returned are by default normalized so that they are rotation and size-invariant.
This can be overridden by calling:
from pyefd import elliptic_fourier_descriptors
coeffs = elliptic_fourier_descriptors(contour, order=10, normalize=False)

Normalization can also be done afterwards:
from pyefd import normalize_efd
coeffs = normalize_efd(coeffs)

OpenCV example
If you are using OpenCV to generate contours, this example shows how to
connect it to pyefd.
import cv2
import numpy
from pyefd import elliptic_fourier_descriptors

# Find the contours of a binary image using OpenCV.
contours, hierarchy = cv2.findContours(
im, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE)

# Iterate through all contours found and store each contour's
# elliptical Fourier descriptor's coefficients.
coeffs = []
for cnt in contours:
# Find the coefficients of all contours
coeffs.append(elliptic_fourier_descriptors(
numpy.squeeze(cnt), order=10))

Using EFD as features
To use these as features, one can write a small wrapper function:
from pyefd import elliptic_fourier_descriptors

def efd_feature(contour):
coeffs = elliptic_fourier_descriptors(contour, order=10, normalize=True)
return coeffs.flatten()[3:]

If the coefficients are normalized, then coeffs[0, 0] = 1.0, coeffs[0, 1] = 0.0 and
coeffs[0, 2] = 0.0, so they can be disregarded when using the elliptic Fourier descriptors as features.
See [1] for more technical details.
Testing
Run tests with with Pytest:
py.test tests.py

The tests include a single image from the MNIST dataset of handwritten digits ([2]) as a contour to use for testing.
Documentation
See ReadTheDocs.
References
[1]: Frank P Kuhl, Charles R Giardina, Elliptic Fourier features of a closed contour, Computer Graphics and Image Processing, Volume 18, Issue 3, 1982, Pages 236-258, ISSN 0146-664X, http://dx.doi.org/10.1016/0146-664X(82)90034-X.
[2]: LeCun et al. (1999): The MNIST Dataset Of Handwritten Digits
Changelog
All notable changes to this project will be documented in this file.
The format is based on Keep a Changelog,
and this project adheres to Semantic Versioning.
1.6.0 (2021-12-09)
Added

Added a demo for 3D surfaces with cylindrical symmetries. (examples/example1.py)

Fixes

Fixes incorrectly plotted curves when no imshow has been called.
Fixes ugly coefficient calculation code.

1.5.1 (2021-01-22)
Added

return_transformation keyword on elliptic_fourier_descriptors method. Merged #11. Fixes #5.

Fixes

Documentation correction. Merged #12.

Removed

Deleted broken example script scikit_image.py.

1.4.1 (2020-09-28)
Added

Added CHANGELOG.md

Changed

Change CI from Azure Devops to Github Actions

1.4.0 (2019-07-27)
Changed

Merged PR #4: Vectorized contour reconstruction function

1.3.0 (2019-06-18)
Changed

Merged PR #2: Numpy vectorized efd
Moved from Travis CI to Azure Pipelines
Replaced rst with markdown

1.2.0 (2018-06-14)
Changed

Updated setup.py
Updated numpy requirement

Added

Added Pipfile
Ran Black on code
Testing on 3.6

1.1.0 (2018-06-13)
Added

New example for OpenCV
Updated documentation

1.0.0 (2016-04-19)
Changed

Deemed stable enough for version 1.0 release

Added

Created documentation.

0.1.2 (2016-02-29)
Changed

Testing with pytest instead of nosetests.

Added

Added Coveralls use.

0.1.1 (2016-02-17)
Fixed

Fixed MANIFEST

Added

Added LICENSE file that was missing.

0.1.0 (2016-02-09)
Added

Initial release