Filtering images

Image filters take an image and produce a new image. Typically, a filter kernel goes from pixel to pixel and computes a new pixel value depending on an old pixel and its neighborhood.

See also

• Filters in scikit-image

We start with a test image and apply a Gaussian blur filter.

import numpy as np
from pyclesperanto_prototype import imshow
from skimage.filters import gaussian
from skimage import filters
import matplotlib.pyplot as plt
from skimage.morphology import disk
from skimage.io import imread

test_image = np.zeros((10,10))
test_image[5,3] = 1
test_image[5,7] = 1
test_image

array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 1., 0., 0., 0., 1., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])

imshow(test_image)

The Gaussian filter takes two important arguments, the image to blur and a sigma parameter. The sigma determines how wide the Gaussian blur should show effects.

blurred = gaussian(test_image, sigma=1)
imshow(blurred)

Let’s compare Gaussian blurred images with different sigma

blurred05 = gaussian(test_image, sigma=0.5)
blurred1 = gaussian(test_image, sigma=1)
blurred2 = gaussian(test_image, sigma=2)
blurred3 = gaussian(test_image, sigma=3)

fig, axs = plt.subplots(1, 4, figsize=(15,15))

imshow(blurred05, plot=axs[0])
imshow(blurred1, plot=axs[1])
imshow(blurred2, plot=axs[2])
imshow(blurred3, plot=axs[3])

Note: If the sigma is larger than the distance between two spots, the spots cannot be differentiated as two local maxima in the blurred image anymore.

Filters with structuring elements

Some filters ask for a structuring element as parameter. In biological/microscopy applications, the disk sturcturing element is most commonly used. To understand it, we should visualize it first. A disk with radius 4 is a 9x9 large image containing black pixels(intensity=0) and disk-shaped pixels with value 1.

imshow(disk(4))

Disks with other radii look like this:

max_radius = 5

fig, axs = plt.subplots(1, max_radius, figsize=(15,15))

for r in range(1, max_radius + 1):
    imshow(disk(r), plot=axs[r - 1])
    axs[r - 1].set_title("Radius " + str(r))

Coming back to our test image, this is how it looks like when we apply a mean filter with different disk radii.

filtered1 = filters.rank.mean(test_image, disk(1))
filtered2 = filters.rank.mean(test_image, disk(2))
filtered3 = filters.rank.mean(test_image, disk(3))

fig, axs = plt.subplots(1, 4, figsize=(15,15))

imshow(test_image, plot=axs[0])
axs[0].set_title('original')

imshow(filtered1, plot=axs[1])
axs[1].set_title('Mean (radius = 1)')

imshow(filtered2, plot=axs[2])
axs[2].set_title('Mean (radius = 2)')

imshow(filtered3, plot=axs[3])
axs[3].set_title('Mean (radius = 3)')

C:\Users\rober\AppData\Local\Temp\ipykernel_8564\198849488.py:1: UserWarning: Possible precision loss converting image of type float64 to uint8 as required by rank filters. Convert manually using skimage.util.img_as_ubyte to silence this warning.
  filtered1 = filters.rank.mean(test_image, disk(1))
C:\Users\rober\AppData\Local\Temp\ipykernel_8564\198849488.py:2: UserWarning: Possible precision loss converting image of type float64 to uint8 as required by rank filters. Convert manually using skimage.util.img_as_ubyte to silence this warning.
  filtered2 = filters.rank.mean(test_image, disk(2))
C:\Users\rober\AppData\Local\Temp\ipykernel_8564\198849488.py:3: UserWarning: Possible precision loss converting image of type float64 to uint8 as required by rank filters. Convert manually using skimage.util.img_as_ubyte to silence this warning.
  filtered3 = filters.rank.mean(test_image, disk(3))

Text(0.5, 1.0, 'Mean (radius = 3)')