Scikit Image − Hessian Filter

Quiz

The Hessian filter is a commonly used technique in image processing for detecting ridge-like structures within an image. These structures can take various forms, such as neurites, tubes, vessels, wrinkles, or rivers. The Hessian filter belongs to a class of ridge filters that rely on the eigenvalues of the Hessian matrix of image intensities to identify ridge structures.

This filter can be used to enhance and analyze the features of interest in an image. The choice of parameters like alpha, beta, and gamma can be adjusted to fine-tune the filter's behavior for a specific application.

The scikit image library provides the hessian() function in the filters module to apply the Hybrid Hessian filter on images.

Using the skimage.filters.hessian() function

The filters.hessian() function is used to filter an image with the Hybrid Hessian filter, primarily designed for detecting continuous edges such as vessels, wrinkles, or rivers.

This filter works on 2-D and 3-D images and is similar to the Frangi filter but it uses an alternative smoothing method. The parameters of this function include:

Syntax

Following is the syntax of this function −

skimage.filters.hessian(image, sigmas=range(1, 10, 2), scale_range=None, scale_step=None, alpha=0.5, beta=0.5, gamma=15, 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 Hessian filter will be applied.
Sigmas (iterable of floats, optional): It specifying the scales of the filter. i.e., np.arange(scale_range[0], scale_range[1], scale_step).
Scale_range (2-tuple of floats, optional): It defines the range of sigmas used.
Scale_step (float, optional): This parameter specifies the step size between sigmas.
Beta (float, optional): The Frangi correction constant, adjusting the filter's sensitivity to deviations from blob-like structures.
Gamma (float, optional): The Frangi correction constant, adjusting the filter's sensitivity to areas with high variance, texture, or structure.
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 returns a filtered image as an ndarray, which is the maximum pixel value across all scales.

Example

This example demonstrates the use of the skimage.filters.hessian() function with its default parameter values −

import matplotlib.pyplot as plt
from skimage.filters import hessian
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 Hessian filter with the default values
filtered_image = hessian(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 Filtered Image
ax[1].imshow(filtered_image, cmap='gray')
ax[1].axis('off')
ax[1].set_title('Hessian Filter Result')

plt.tight_layout()
plt.show()

Output

Example

The following example demonstrates the use of the Hessian filter using the skimage.filters.hessian() function on an image with different sigmas to enhance and visualize structures in an image −

from skimage import io
from skimage import color
from skimage.filters import hessian
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 Hessian filter with differnt sigmas 
result_hessian_black_ridges = hessian(image, sigmas=[1], black_ridges=True)
result_hessian_sigmas_black_ridges = hessian(image, sigmas=range(1, 5), black_ridges=True)

# Plot the original and filtered 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_hessian_black_ridges, cmap='gray')
ax[1].axis('off')
ax[1].set_title('Hessian Filter (black_ridges=True)\n \N{GREEK SMALL LETTER SIGMA}=[1]')

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

# 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_hessian_black_ridges, cmap='gray')
ax[4].axis('off')
ax[4].set_title('Hessian Filter (black_ridges=True)\n \N{GREEK SMALL LETTER SIGMA}=[1]')

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

plt.tight_layout()
plt.show()

Output

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