Mahotas - Otsu's Method

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Otsu's method is a technique used for image segmentation to separate the foreground from the background. It works by finding a threshold value that maximizes the inter−class variance.

The inter−class variance is a measure of the separation between the foreground and the background regions.

The threshold value that maximizes the inter−class variance is considered the optimal threshold value for image segmentation.

Otsu's Method in Mahotas

In Mahotas, we can utilize the thresholding.otsu() function to calculate the threshold value using Otsu's method. The function operates in the following manner −

• First it finds the histogram of the image. The histogram is a plot of the number of pixels in the image at each grayscale level.

• Next, the threshold value is set to the average grayscale value of the image.

• Then, the inter−class variance is calculated for the current threshold value.

• The threshold value is then increased, and the inter−class variance is recalculated.

Steps 2 to 4 are repeated until an optimal threshold value is reached.

The mahotas.thresholding.otsu() function

The mahotas.thresholding.otsu() function takes a grayscale image as input and returns its threshold value calculated using Otsu's method. The pixels of the grayscale image are then compared to the threshold value to create a segmented image.

Syntax

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

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

Where,

• img − It is the input grayscale image.

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

Example

In the following example, we are using mh.thresholding.otsu() 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('sea.bmp')
# Converting it to grayscale
image = mh.colors.rgb2gray(image).astype(np.uint8)
# Calculating threshold value using Otsu method
otsu_threshold = mh.thresholding.otsu(image)
# Creating image from the threshold value
final_image = image > otsu_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('Otsu 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 Otsu's threshold value by ignoring the zero valued pixels. 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 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 the value zero when calculating the threshold value using Otsu's method.

import mahotas as mh
import numpy as np
import matplotlib.pyplot as mtplt
# Loading the image
image = mh.imread('tree.tiff')
# Converting it to grayscale
image = mh.colors.rgb2gray(image).astype(np.uint8)
# Calculating threshold value using Otsu method
otsu_threshold = mh.thresholding.otsu(image, ignore_zeros=True)
# Creating image from the threshold value
final_image = image > otsu_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('Otsu 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 −