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