.. _example_plot_edge_filter.py:


==============
Edge operators
==============

Edge operators are used in image processing within edge detection algorithms.
They are discrete differentiation operators, computing an approximation of the
gradient of the image intensity function.



.. code-block:: python

	import numpy as np
	import matplotlib.pyplot as plt
	
	from skimage.data import camera
	from skimage.filters import roberts, sobel, scharr
	
	
	image = camera()
	edge_roberts = roberts(image)
	edge_sobel = sobel(image)
	
	fig, (ax0, ax1) = plt.subplots(ncols=2)
	
	ax0.imshow(edge_roberts, cmap=plt.cm.gray)
	ax0.set_title('Roberts Edge Detection')
	ax0.axis('off')
	
	ax1.imshow(edge_sobel, cmap=plt.cm.gray)
	ax1.set_title('Sobel Edge Detection')
	ax1.axis('off')
	
	plt.tight_layout()
	
	

.. image:: images/plot_edge_filter_1.png

Different operators compute different finite-difference approximations of the
gradient. For example, the Scharr filter results in a better rotational
variance than other filters such as the Sobel filter [1]_ [2]_. The difference
between the two filters is illustrated below on an image that is the
discretization of a rotation-invariant continuous function. The discrepancy
between the two filters is stronger for regions of the image where the
direction of the gradient is close to diagonal, and for regions with high
spatial frequencies.

.. [1] http://en.wikipedia.org/wiki/Sobel_operator#Alternative_operators

.. [2] B. Jaehne, H. Scharr, and S. Koerkel. Principles of filter design. In
       Handbook of Computer Vision and Applications. Academic Press, 1999.


.. code-block:: python

	
	x, y = np.ogrid[:100, :100]
	# Rotation-invariant image with different spatial frequencies
	img = np.exp(1j * np.hypot(x, y)**1.3 / 20.).real
	
	edge_sobel = sobel(img)
	edge_scharr = scharr(img)
	
	fig, ((ax0, ax1), (ax2, ax3)) = plt.subplots(nrows=2, ncols=2)
	
	ax0.imshow(edge_sobel, cmap=plt.cm.gray)
	ax0.set_title('Sobel Edge Detection')
	ax0.axis('off')
	
	ax1.imshow(edge_scharr, cmap=plt.cm.gray)
	ax1.set_title('Scharr Edge Detection')
	ax1.axis('off')
	
	ax2.imshow(img, cmap=plt.cm.gray)
	ax2.set_title('Original image')
	ax2.axis('off')
	
	ax3.imshow(edge_scharr - edge_sobel, cmap=plt.cm.jet)
	ax3.set_title('difference (Scharr - Sobel)')
	ax3.axis('off')
	
	plt.tight_layout()
	
	plt.show()
	
	

.. image:: images/plot_edge_filter_2.png



**Python source code:** :download:`download <plot_edge_filter.py>`
(generated using ``skimage`` |version|)



**IPython Notebook:** :download:`download <./notebook/plot_edge_filter.ipynb>`
(generated using ``skimage`` |version|)

