Scikit Image − Sato Filter

The Sato tubeness filter is an image processing algorithm designed to enhance ridge-like structures in images. The structures include objects like blood vessels, neurites, and other tube-like structures. The filter was introduced by Sato et al. in 1998, the primary purpose of the Sato tubeness filter is to enhance and highlight ridge-like structures within images. The Sato tubeness filter is often considered a faster alternative to another popular vessel enhancement filter called the Frangi filter.

The Sato tubeness filter belongs to a class of ridge filters that rely on the eigenvalues of the Hessian matrix of image intensities to identify ridge structures.

The scikit image library provides the sato() function in the filters module to apply the Sato tubeness filter on images.

Using the skimage.filters.sato() function

The filters.sato() function is used to filter an image with the Sato tubeness filter. The Sato tubeness filter is designed for detecting continuous ridges in an image. It is only defined for 2-D and 3-D images. It calculates the eigenvectors of the Hessian matrix to analyze the local structure of an image region.

Syntax

Following is the syntax of this function −

skimage.filters.sato(image, sigmas=range(1, 10, 2), black_ridges=True, mode='reflect', cval=0)

Parameters

The function accepts the following parameters −

• Image ((N, M[, P]) ndarray): This parameter is the input image on which the Sato tubeness filter will be applied.
• Sigmas (iterable of floats, optional): Specify the scales of the filter.
• Black_ridges (boolean, optional): The default value is True, determining whether the filter detects black ridges (True) or white ridges (False).
• Mode (string, optional): This parameter specifies how to handle values outside the image borders, with options like 'constant', 'reflect', 'wrap', 'nearest', or 'mirror'.
• Cval (float, optional): This is used in conjunction with mode 'constant' to specify the value outside the image boundaries.

Return value

The function then returns a filtered image represented as a NumPy ndarray. The result is the maximum value of pixels across all the scales, which highlights the detected ridges or structures in the image.

Example

This example applies the skimage.filters.sato() function on an image with its default parameter values −

import matplotlib.pyplot as plt
from skimage.filters import sato
from skimage import io, color

# Load the input image 
in_image = io.imread('Images/tree.jpg')
x_0 = 250
y_0 = 100
width = 250
height = 150

# Crop the image to the specified region and convert it to grayscale
image = color.rgb2gray(in_image[y_0:(y_0 + height), x_0:(x_0 + width)])

# Apply the Sato filter with the default values
filtered_image = sato(image)

# Plot the original and filtered images
fig, axes = plt.subplots(1, 2, figsize=(10, 5))
ax = axes.ravel()

# Display the Original Image
ax[0].imshow(image, cmap='gray')
ax[0].set_title('Original Image')
ax[0].axis('off')

# Display the Sato Filter Result
ax[1].imshow(filtered_image, cmap='gray')
ax[1].axis('off')
ax[1].set_title('Sato Filter Result')

plt.tight_layout()
plt.show()

Output

Example

The following example demonstrates the use of the Sato tubeness filter using the skimage.filters.sato() function on an image with different sigmas to enhance and visualize tube-like structures in an image −

from skimage import io
from skimage import color
from skimage.filters import sato
import matplotlib.pyplot as plt

# Load the input image
in_image = io.imread('Images/tree.jpg')
x_0 = 250
y_0 = 100
width = 250
height = 150

# Crop the image to the specified region and convert it to grayscale
image = color.rgb2gray(in_image[y_0:(y_0 + height), x_0:(x_0 + width)])

# Apply the Sato tubeness filter with black_ridges=True
result_black_ridges = sato(image, black_ridges=True, sigmas=[1])
result_black_ridges_sigmas = sato(image, black_ridges=True, sigmas=range(1, 5))

# Apply the Sato tubeness filter with black_ridges=False
result_white_ridges = sato(image, black_ridges=False, sigmas=[1])
result_white_ridges_sigmas = sato(image, black_ridges=False, sigmas=range(1, 5))

# Plot the original, filtered (both black_ridges=True and black_ridges=False) images
fig, axes = plt.subplots(2, 3, figsize=(10, 5))
ax = axes.ravel()

# Display the Original Image
ax[0].imshow(image, cmap='gray')
ax[0].set_title('Original Image')
ax[0].axis('off')

# Display the Result with black_ridges=True
ax[1].imshow(result_black_ridges, cmap='gray')
ax[1].axis('off')
ax[1].set_title('Sato Filter (black_ridges=True)\n \N{GREEK SMALL LETTER SIGMA}=[1]')

# Display the Result with black_ridges=False
ax[2].imshow(result_white_ridges, cmap='gray')
ax[2].axis('off')
ax[2].set_title('Sato Filter (black_ridges=False)\n \N{GREEK SMALL LETTER SIGMA} =[1]')

# Display the Original Image again (for the second row)
ax[3].imshow(image, cmap='gray')
ax[3].axis('off')
ax[3].set_title('Original Image')

# Display the Result with black_ridges=True
ax[4].imshow(result_black_ridges_sigmas, cmap='gray')
ax[4].axis('off')
ax[4].set_title('Sato Filter (black_ridges=True)\n \N{GREEK SMALL LETTER SIGMA} =[1,2,3,4]')

# Display the Result with black_ridges=False
ax[5].imshow(result_white_ridges_sigmas, cmap='gray')
ax[5].axis('off')
ax[5].set_title('Sato Filter (black_ridges=False)\n \N{GREEK SMALL LETTER SIGMA} =[1,2,3,4]')

plt.tight_layout()
plt.show()

Output