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
10 Dec 18, 2022
637 Jan 04, 2023
70 Jan 01, 2023
319 Dec 30, 2022
49 Dec 01, 2022
60 Dec 16, 2022
3 Jun 15, 2022
781 Jan 03, 2023
14 Oct 10, 2022
152 Oct 27, 2022
715 Nov 05, 2022
23 Oct 08, 2022
293 Dec 22, 2022
28 Nov 29, 2022
8 Dec 04, 2022
22 Dec 09, 2022
36 Dec 28, 2022
98 Dec 30, 2022
7.1k Jan 03, 2023
136 Jan 04, 2023