Skip to content
/ pyefd Public

Python implementation of "Elliptic Fourier Features of a Closed Contour"

License

Notifications You must be signed in to change notification settings

hbldh/pyefd

Folders and files

NameName
Last commit message
Last commit date

Latest commit

Aug 28, 2023
54f5e83 · Aug 28, 2023

History

66 Commits
Aug 28, 2023
Aug 28, 2023
Dec 9, 2021
Feb 29, 2016
Feb 7, 2016
Aug 28, 2023
Dec 9, 2021
Sep 28, 2020
Jun 18, 2019
Sep 28, 2020
Dec 9, 2021
Aug 28, 2023
Jul 27, 2019
Feb 29, 2016
Dec 9, 2021
Jan 22, 2021

Repository files navigation

PyEFD

Build and Test Documentation Status image image image

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