.. _example_plot_regional_maxima.py:


=========================
Filtering regional maxima
=========================

Here, we use morphological reconstruction to create a background image, which
we can subtract from the original image to isolate bright features (regional
maxima).

First we try reconstruction by dilation starting at the edges of the image. We
initialize a seed image to the minimum intensity of the image, and set its
border to be the pixel values in the original image. These maximal pixels will
get dilated in order to reconstruct the background image.



.. code-block:: python

	import numpy as np
	from scipy.ndimage import gaussian_filter
	import matplotlib.pyplot as plt
	
	from skimage import data
	from skimage import img_as_float
	from skimage.morphology import reconstruction
	
	# Convert to float: Important for subtraction later which won't work with uint8
	image = img_as_float(data.coins())
	image = gaussian_filter(image, 1)
	
	seed = np.copy(image)
	seed[1:-1, 1:-1] = image.min()
	mask = image
	
	dilated = reconstruction(seed, mask, method='dilation')
	
	

Subtracting the dilated image leaves an image with just the coins and a flat,
black background, as shown below.


.. code-block:: python

	
	fig, (ax1, ax2, ax3) = plt.subplots(ncols=3, figsize=(8, 2.5))
	
	ax1.imshow(image)
	ax1.set_title('original image')
	ax1.axis('off')
	
	ax2.imshow(dilated, vmin=image.min(), vmax=image.max())
	ax2.set_title('dilated')
	ax2.axis('off')
	
	ax3.imshow(image - dilated)
	ax3.set_title('image - dilated')
	ax3.axis('off')
	
	fig.tight_layout()
	
	


.. image:: images/plot_regional_maxima_1.png

Although the features (i.e. the coins) are clearly isolated, the coins
surrounded by a bright background in the original image are dimmer in the
subtracted image. We can attempt to correct this using a different seed image.

Instead of creating a seed image with maxima along the image border, we can use
the features of the image itself to seed the reconstruction process. Here, the
seed image is the original image minus a fixed value, ``h``.


.. code-block:: python

	
	h = 0.4
	seed = image - h
	dilated = reconstruction(seed, mask, method='dilation')
	hdome = image - dilated
	
	

To get a feel for the reconstruction process, we plot the intensity of the
mask, seed, and dilated images along a slice of the image (indicated by red
line).


.. code-block:: python

	
	fig, (ax1, ax2, ax3) = plt.subplots(ncols=3, figsize=(8, 2.5))
	
	yslice = 197
	
	ax1.plot(mask[yslice], '0.5', label='mask')
	ax1.plot(seed[yslice], 'k', label='seed')
	ax1.plot(dilated[yslice], 'r', label='dilated')
	ax1.set_ylim(-0.2, 2)
	ax1.set_title('image slice')
	ax1.set_xticks([])
	ax1.legend()
	
	ax2.imshow(dilated, vmin=image.min(), vmax=image.max())
	ax2.axhline(yslice, color='r', alpha=0.4)
	ax2.set_title('dilated')
	ax2.axis('off')
	
	ax3.imshow(hdome)
	ax3.axhline(yslice, color='r', alpha=0.4)
	ax3.set_title('image - dilated')
	ax3.axis('off')
	
	fig.tight_layout()
	plt.show()
	
	

.. image:: images/plot_regional_maxima_2.png

As you can see in the image slice, each coin is given a different baseline
intensity in the reconstructed image; this is because we used the local
intensity (shifted by ``h``) as a seed value. As a result, the coins in the
subtracted image have similar pixel intensities. The final result is known as
the h-dome of an image since this tends to isolate regional maxima of height
``h``. This operation is particularly useful when your images are unevenly
illuminated.



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



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

