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https://github.com/hbldh/pyefd
Python implementation of "Elliptic Fourier Features of a Closed Contour"
https://github.com/hbldh/pyefd
contours feature-extraction features fourier-series numpy python
Last synced: 3 days ago
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Python implementation of "Elliptic Fourier Features of a Closed Contour"
- Host: GitHub
- URL: https://github.com/hbldh/pyefd
- Owner: hbldh
- License: mit
- Created: 2016-02-07T22:59:34.000Z (almost 9 years ago)
- Default Branch: master
- Last Pushed: 2023-08-28T12:33:23.000Z (over 1 year ago)
- Last Synced: 2024-12-09T19:53:34.224Z (13 days ago)
- Topics: contours, feature-extraction, features, fourier-series, numpy, python
- Language: Python
- Homepage: http://pyefd.readthedocs.org/
- Size: 250 KB
- Stars: 86
- Watchers: 4
- Forks: 15
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE
Awesome Lists containing this project
README
PyEFD
=====
[](https://github.com/hbldh/pyefd/actions?query=workflow%3A%22Build+and+Test%22)
[](http://pyefd.readthedocs.org/en/latest/?badge=latest)
[](https://pypi.python.org/pypi/pyefd/)
[](https://pypi.python.org/pypi/pyefd/)
[](https://coveralls.io/github/hbldh/pyefd?branch=master)
An Python/NumPy implementation of a method for approximating a contour with a Fourier series, as described in [1].
Installation
------------
```bash
pip install pyefd
```
Usage
-----
Given a closed contour of a shape, generated by e.g. [scikit-image](http://scikit-image.org/) or
[OpenCV](http://opencv.org/), this package can fit a
[Fourier series](https://en.wikipedia.org/wiki/Fourier_series) approximating the shape of the contour.
### General usage examples
This section describes the general usage patterns of `pyefd`.
```python
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:
```python
from pyefd import elliptic_fourier_descriptors
coeffs = elliptic_fourier_descriptors(contour, order=10, normalize=False)
```
Normalization can also be done afterwards:
```python
from pyefd import normalize_efd
coeffs = normalize_efd(coeffs)
```
### OpenCV example
If you are using [OpenCV](http://opencv.org/) to generate contours, this example shows how to
connect it to `pyefd`.
```python
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:
```python
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](http://pytest.org/latest/):
```bash
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](http://pyefd.readthedocs.org/).
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://www.sci.utah.edu/~gerig/CS7960-S2010/handouts/Kuhl-Giardina-CGIP1982.pdf)
[2]: [LeCun et al. (1999): The MNIST Dataset Of Handwritten Digits](http://yann.lecun.com/exdb/mnist/)