Mahotas - Riddler-Calvard Method

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The Riddler−Calvard method is a technique used for segmenting an image into foreground and background regions. It groups the pixels of the image to minimize the within−cluster variance when calculating threshold value.

The within−cluster variance measures how spread out the pixel values are within a group. A low within−cluster variance indicates that the pixel values are close together, while a high within−cluster variance indicates that the pixel values are spread out.

Riddler-Calvard Method in Mahotas

In Mahotas, we use the thresholding.rc() function to calculate the threshold value of an image using the Riddler−Calvard technique. The function operates in the following manner −

• It calculates the mean and variance of the two clusters − the foreground and the background. The mean value is the average value of all the pixels and the variance is a measure of spread of the pixels.

• Next, it chooses a threshold value that minimizes the within−cluster variance.

• It then assigns each pixel to the cluster with the lower variance.

Steps 2 and 3 continuously repeated until the threshold value is calculated. This value is then used to segment an image into the foreground and the background.

The mahotas.thresholding.rc() function

The mahotas.thresholding.rc() function takes a grayscale image as input and returns its threshold value calculated using the Riddler−Calvard technique.

The pixels of the grayscale image are then compared to the threshold value to create a binary image.

Syntax

Following is the basic syntax of the rc() function in mahotas −

mahotas.thresholding.rc(img, ignore_zeros=False)

Where,

• img − It is the input grayscale image.

• ignore_zeros (optional) − It is a flag which specifies whether to ignore zero valued pixels (default is false).

Example

In the following example, we are using the mh.thresholding.rc() function to find the threshold value.

import mahotas as mh
import numpy as np
import matplotlib.pyplot as mtplt
# Loading the image
image = mh.imread('sun.png')
# Converting it to grayscale
image = mh.colors.rgb2gray(image).astype(np.uint8)
# Calculating threshold value using Riddler-Calvard method
rc_threshold = mh.thresholding.rc(image)
# Creating image from the threshold value
final_image = image > rc_threshold
# Creating a figure and axes for subplots
fig, axes = mtplt.subplots(1, 2)
# Displaying the original image
axes[0].imshow(image, cmap='gray')
axes[0].set_title('Original Image')
axes[0].set_axis_off()
# Displaying the threshold image
axes[1].imshow(final_image, cmap='gray')
axes[1].set_title('Riddler-Calvard Threshold Image')
axes[1].set_axis_off()
# Adjusting spacing between subplots
mtplt.tight_layout()
# Showing the figures
mtplt.show()

Output

Following is the output of the above code −

Ignoring the Zero Valued Pixels

We can also find the Riddler−Calvard threshold value by ignoring the zero valued pixels. The zero valued pixels are pixels that have an intensity value of 0.

They usually represent the background pixels of an image, but in some images, they may also represent noise.

In grayscale images, zero valued pixels are pixels represented by the color 'black'.

To exclude zero valued pixels when calculating the threshold value in mahotas, we can set the ignore_zeros parameter to the boolean value 'True'.

Example

In the example mentioned below, we are ignoring pixels with value zero when calculating the threshold value using the Riddler−Calvard method.

import mahotas as mh
import numpy as np
import matplotlib.pyplot as mtplt
# Loading the image
image = mh.imread('nature.jpeg')
# Converting it to grayscale
image = mh.colors.rgb2gray(image).astype(np.uint8)
# Calculating threshold value using Riddler-Calvard method
rc_threshold = mh.thresholding.rc(image, ignore_zeros=True)
# Creating image from the threshold value
final_image = image > rc_threshold
# Creating a figure and axes for subplots
fig, axes = mtplt.subplots(1, 2)
# Displaying the original image
axes[0].imshow(image, cmap='gray')
axes[0].set_title('Original Image')
axes[0].set_axis_off()
# Displaying the threshold image
axes[1].imshow(final_image, cmap='gray')
axes[1].set_title('Riddler-Calvard Threshold Image')
axes[1].set_axis_off()
# Adjusting spacing between subplots
mtplt.tight_layout()
# Showing the figures
mtplt.show()

Output

After executing the above code, we get the following output −