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. scikitimage 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 sizeinvariant. 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 EFD as features, one can write a small wrapper function:
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:
$ python setup.py test
or with Pytest:
$ py.test tests.py
The tests includes a single image from the MNIST dataset of handwritten digits ([2]) as a contour to use for testing.
References¶
[2]  (1, 2) LeCun et al. (1999): The MNIST Dataset Of Handwritten Digits 
API¶
A Python implementation of the method described in [3] and [4] for calculating Fourier coefficients for characterizing closed contours.
References¶
[3]  (1, 2, 3, 4) F. P. Kuhl and C. R. Giardina, “Elliptic Fourier Features of a Closed Contour,” Computer Vision, Graphics and Image Processing, Vol. 18, pp. 236258, 1982. 
[4]  (1, 2, 3, 4) Oivind Due Trier, Anil K. Jain and Torfinn Taxt, “Feature Extraction Methods for Character Recognition  A Survey”, Pattern Recognition Vol. 29, No.4, pp. 641662, 1996 
Created by hbldh <henrik.blidh@nedomkull.com> on 20160130.

pyefd.
calculate_dc_coefficients
(contour)¶ Calculate the \(A_0\) and \(C_0\) coefficients of the elliptic Fourier series.
Parameters: contour (numpy.ndarray) – A contour array of size [M x 2]
.Returns: The \(A_0\) and \(C_0\) coefficients. Return type: tuple

pyefd.
elliptic_fourier_descriptors
(contour, order=10, normalize=False)¶ Calculate elliptical Fourier descriptors for a contour.
Parameters:  contour (numpy.ndarray) – A contour array of size
[M x 2]
.  order (int) – The order of Fourier coefficients to calculate.
 normalize (bool) – If the coefficients should be normalized; see references for details.
Returns: A
[order x 4]
array of Fourier coefficients.Return type: numpy.ndarray
 contour (numpy.ndarray) – A contour array of size

pyefd.
normalize_efd
(coeffs, size_invariant=True)¶ Normalizes an array of Fourier coefficients.
Parameters:  coeffs (numpy.ndarray) – A
[n x 4]
Fourier coefficient array.  size_invariant (bool) – If size invariance normalizing should be done as well.
Default is
True
.
Returns: The normalized
[n x 4]
Fourier coefficient array.Return type: numpy.ndarray
 coeffs (numpy.ndarray) – A

pyefd.
plot_efd
(coeffs, locus=(0.0, 0.0), image=None, contour=None, n=300)¶ Plot a
[2 x (N / 2)]
grid of successive truncations of the series.Note
Requires matplotlib!
Parameters:

pyefd.
reconstruct_contour
(coeffs, locus=(0, 0), num_points=300)¶ Returns the contour specified by the coefficients.
Parameters: Returns: A list of x,y coordinates for the reconstructed contour.
Return type: numpy.ndarray