Mahotas - Zernike Features

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Zernike features are a set of mathematical values that describe the shape of objects in an image. These value reflects specific details about the shape, such as its roundness, symmetry, or the presence of certain patterns.

The Zernike features have some special properties that make them useful for shape analysis. For example, they can describe the shape regardless of its size, meaning that the features remain the same even if the shape is rotated or scaled.

This property helps in recognizing objects under different conditions.

Zernike features work by breaking down the shape into smaller pieces using mathematical functions called Zernike polynomials. These polynomials act like building blocks, and by combining them, we can recreate and represent the shape of the object.

Zernike Features in Mahotas

To calculate the Zernike features in mahotas, we can use the mahotas.features.zernike() function.

In Mahotas, Zernike features are calculated by performing the following steps −

Step1 − Generate a set of Zernike polynomials, which are special mathematical functions representing various shapes and contours. These polynomials act as building blocks for analyzing the object's shape.

Step2 − Compute Zernike moments by projecting the shape of the object onto the Zernike polynomials. These moments capture important shape characteristics.

Step3 − Extract the Zernike features from the computed moments, which represent the essential shape information.

The mahotas.features.zernike() function

The mahotas.features.zernike() function takes three arguments: the image object, the maximum radius for the Zernike polynomials, and the number of features (degree) to compute. The function returns a 1−D array of the Zernike features for the image.

The degree of a Zernike moment is a measure of the complexity of the moment. The higher the degree, the more complex the moment.

Syntax

Following is the basic syntax of the mahotas.features.zernike() function − 

mahotas.features.zernike(im, degree, radius, cm={center_of_mass(im)})

Where,

  • im − It is the input image on which the Zernike moments will be computed.

  • degree − It specifies the maximum number of the Zernike moments to be calculated.

  • radius − It defines the radius of the circular region, in pixels, over which the Zernike moments will be calculated. The area outside the circle defined by this radius, centered around the center of mass, is ignored.

  • cm (optional) − It specifies the center of mass of the image. By default, the center of mass of the image is used.

Example

Following is the basic example to calculate the Zernike features for shape recognition of an image − 

import mahotas as mh
# Load images of shapes
image1 = mh.imread('sun.png', as_grey=True)
# Compute Zernike features
features = mh.features.zernike(image1, degree=8, radius=10)
# Printing the features for shape recognition
print(features)
Output

After executing the above code, we get the output as follows − 

[0.31830989 0.00534998 0.00281258 0.0057374  0.01057919 0.00429721
 0.00178094 0.00918145 0.02209622 0.01597089 0.00729495 0.00831211
 0.00364554 0.01171028 0.02789188 0.01186194 0.02081316 0.01146935
 0.01319499 0.03367388 0.01580632 0.01314671 0.02947629 0.01304526
 0.00600012]

Using Custom Center of Mass

The center of mass of an image is the point in the image where the mass is evenly distributed. The custom center of mass is a point in an image that is not necessarily the center of mass of the image.

This can be useful in cases where you want to use a different center of mass for your calculations.

For example, you might want to use the custom center of mass of an object in an image to calculate the Zernike moments of the object.

To calculate the Zernike moments of an image using a custom center of mass in mahotas, we need to pass the cm parameter to the mahotas.features.zernike() function.

The cm parameter takes a tuple of two numbers, which represent the coordinates of the custom center of mass.

Example

In here, we are trying to calculate the Zernike features of an image using the custom center of mass − 

import mahotas
import numpy as np
# Load the image
image = mahotas.imread('nature.jpeg', as_grey = True)
# Calculate the center of mass of the image
center_of_mass = np.array([100, 100])
# Calculate the Zernike features of the image, using the custom center of mass
zernike_features = mahotas.features.zernike(image, degree= 5, radius = 5,
cm=center_of_mass)
# Print the Zernike features
print(zernike_features)

Output

Following is the output of the above code − 

[3.18309886e-01 3.55572603e-04 3.73132619e-02 5.98944983e-04
3.23622041e-04  1.72293481e-04 9.16757235e-02 3.35704966e-04
7.09426259e-02  1.17847972e-04 2.12625026e-04 3.06537827e-04]

Calculating Zernike Features of Multiple Images

We can also calculate the Zernike features of multiple images in different formats. Following is the approach to achieve this −

  • Creates an empty list.

  • Use a for loop to iterate over the list of images.

  • Calculate the Zernike features of each image.

The features.zernike() function returns a vector of Zernike moments, which is then appended to the list of Zernike features.

Example

Now, we are trying to calculate the Zernike features of multiple images of different formats altogether − 

import mahotas
import numpy as np
# Load the images
images = [mahotas.imread('sun.png', as_grey = True),
mahotas.imread('nature.jpeg', as_grey = True), mahotas.imread('tree.tiff',
as_grey = True)]
# Calculate the Zernike features of the images
zernike_features = []
for image in images:
   zernike_features.append(mahotas.features.zernike(image, degree=2, radius =
2))
# Print the Zernike features
print(zernike_features)

Output

Output of the above code is as follows − 

[array([0.31830989, 0.05692079, 0.10311168, 0.01087613]), array([0.31830989, 0.02542476, 0.11556386, 0.01648607]), array([0.31830989, 0.12487805, 0.07212079, 0.03351757])]
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