An Python/NumPy implementation of a method for approximating a contour with a Fourier series, as described in [1].
pip install pyefdGiven 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.
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)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))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.
Run tests with with Pytest:
py.test tests.pyThe tests include a single image from the MNIST dataset of handwritten digits ([2]) as a contour to use for testing.
See ReadTheDocs.
[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
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