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OPENCV-PYTHON | OTSU and TRIANGLE Thresholding | Full Mathematics + CODE Explained | Important !

Introduction:

Image thresholding is a pivotal technique in image processing, playing a crucial role in enhancing features, segmenting objects, and simplifying complex images. In this article, we delve into two advanced thresholding methods in OpenCV-Python: Otsu and Triangle. Understanding the mathematics behind these methods is essential for leveraging their power in various computer vision applications.

 

Flow of Article:

  1. What is Thresholding
  2. Understanding Otsu Thresholding
  3. Understanding Triangle Thresholding
  4. Coding both the processes

Video explanation :

 

Thresholding Fundamentals:

Thresholding involves converting an image into a binary format, where pixels are categorized as either foreground or background based on their intensity values. This process simplifies complex images, making subsequent image analysis more manageable.

 

Otsu’s Method:

Otsu’s method is an adaptive thresholding technique that automatically determines the optimal threshold value by maximizing the variance between two classes of pixels: foreground and background. Mathematically, Otsu’s threshold (T_Otsu) is calculated using the following equations:

Algorithm for Otsu’s Method:

  1. Compute the histogram of the image.
  2. Normalize the histogram to obtain probabilities.
  3. Initialize variables for total pixels, sum of intensities, sum of squared intensities, and maximum variance.
  4. Iterate through all possible threshold values: a. Update the variables based on the current threshold. b. Calculate the variance between classes. c. Update the threshold if the variance is greater than the maximum variance.
  5. The final threshold is the one that maximizes the variance.

 

Triangle Method:

The Triangle method is a non-parametric thresholding technique that computes the threshold as the point where a line connecting the histogram’s peak to the maximum intensity intersects with the histogram. Mathematically, the Triangle threshold (T_Triangle) is calculated as:

Algorithm for Triangle Method:

  1. Compute the histogram of the image.

  2. Find the peak of the histogram and the position of the maximum intensity.

  3. Calculate the slope of the line connecting the peak to the maximum intensity.
  4. Determine the threshold where the line intersects the histogram.

By understanding the mathematical foundations and algorithms of Otsu and Triangle thresholding methods, one can effectively utilize these techniques in OpenCV-Python for precise image segmentation and analysis. The code snippets below demonstrate the implementation of both methods.

Code for Otsu’s Method:

import cv2
import numpy as np

# Read the image in grayscale
image = cv2.imread(‘sample_image.jpg’, 0)

# Apply Otsu’s thresholding
_, otsu_thresholded = cv2.threshold(image, 0, 255, cv2.THRESH_BINARY + cv2.THRESH_OTSU)

# Display the original and Otsu-thresholded images
cv2.imshow(‘Original Image’, image)
cv2.imshow(‘Otsu Thresholding’, otsu_thresholded)
cv2.waitKey(0)
cv2.destroyAllWindows()

Code for Triangle Method:

import cv2
import numpy as np
from scipy.signal import find_peaks

# Read the image in grayscale
image = cv2.imread(‘sample_image.jpg’, 0)

# Compute the histogram
hist, bins = np.histogram(image.flatten(), 256, [0, 256])

# Find the peak of the histogram
peaks, _ = find_peaks(hist)

# Calculate Triangle threshold
triangle_threshold = (peaks[0] + np.argmax(hist[peaks[0]:])) // 2

# Apply Triangle thresholding
_, triangle_thresholded = cv2.threshold(image, triangle_threshold, 255, cv2.THRESH_BINARY)

# Display the original and Triangle-thresholded images
cv2.imshow(‘Original Image’, image)
cv2.imshow(‘Triangle Thresholding’, triangle_thresholded)
cv2.waitKey(0)
cv2.destroyAllWindows()

Conclusion

These code snippets showcase the practical implementation of Otsu and Triangle thresholding methods in OpenCV-Python, providing a hands-on understanding of their capabilities in image segmentation.

For further exploration and reference, consider consulting the official [OpenCV documentation] and the [Python documentation]. Engaging with the OpenCV community on platforms like [GitHub] and [Stack Overflow] can also offer valuable insights and support.

Mastering these thresholding techniques opens up a realm of possibilities for image analysis and computer vision applications, making them essential tools in a developer’s toolkit. Keep experimenting, stay curious, and embrace the transformative power of image thresholding in OpenCV-Python.