Morphology is the study of shapes. In image processing, some simple operations can get you a long way. The first things to learn are erosion and dilation. In erosion, we look at a pixel’s local neighborhood and replace the value of that pixel with the minimum value of that neighborhood. In dilation, we instead choose the maximum.
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import numpy as np
from matplotlib import pyplot as plt, cm
%matplotlib inline
import skdemo
plt.rcParams['image.cmap'] = 'cubehelix'
plt.rcParams['image.interpolation'] = 'none'
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image = np.array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]], dtype=np.uint8)
plt.imshow(image);
The documentation for scikit-image's morphology module is here.
Importantly, we must use a structuring element, which defines the local
neighborhood of each pixel. To get every neighbor (up, down, left, right, and
diagonals), use morphology.square; to avoid diagonals, use
morphology.diamond:
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from skimage import morphology
sq = morphology.square(width=3)
dia = morphology.diamond(radius=1)
print(sq)
print(dia)
The central value of the structuring element represents the pixel being considered, and the surrounding values are the neighbors: a 1 value means that pixel counts as a neighbor, while a 0 value does not. So:
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skdemo.imshow_all(image, morphology.erosion(image, sq), shape=(1, 2))
and
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skdemo.imshow_all(image, morphology.dilation(image, sq))
and
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skdemo.imshow_all(image, morphology.dilation(image, dia))
Erosion and dilation can be combined into two slightly more sophisticated operations, opening and closing. Here's an example:
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image = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], np.uint8)
plt.imshow(image);
What happens when run an erosion followed by a dilation of this image?
What about the reverse?
Try to imagine the operations in your head before trying them out below.
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skdemo.imshow_all(image, morphology.opening(image, sq)) # erosion -> dilation
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skdemo.imshow_all(image, morphology.closing(image, sq)) # dilation -> erosion
Exercise: use morphological operations to remove noise from a binary image.
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from skimage import data, color
hub = color.rgb2gray(data.hubble_deep_field()[350:450, 90:190])
plt.imshow(hub);
Remove the smaller objects to retrieve the large galaxy using a boolean array, and then use skimage.exposure.histogram and plt.plot to show the light distribution from the galaxy.
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%reload_ext load_style
%load_style ../themes/tutorial.css