🌓 Thresholding in Digital Image Processing

B.Sc. Computer Science Honours | Image Segmentation

📘 1. Introduction

Thresholding is one of the simplest and most important techniques used in Digital Image Processing for separating an object from its background.

The basic idea is to compare the intensity value of each pixel with a selected threshold value T.

Basic idea: Pixels are divided into different classes according to whether their intensity is below or above the threshold.

Grayscale
Image

→

Threshold
T

→

Pixel
Comparison

→

Binary
Image

⚙️ 2. Basic Principle

Let the grayscale intensity of a pixel be represented by f(x,y) and let T be the threshold.

g(x,y) = { 1, if f(x,y) ≥ T
    0, if f(x,y) < T }

Here:

• f(x,y) = original grayscale pixel value
• T = threshold value
• g(x,y) = thresholded output
• 1 = foreground/object
• 0 = background

For an 8-bit grayscale image, pixel values normally range from 0 to 255.

🔢 3. Numerical Example

Consider the following grayscale pixel values:

20, 60, 100, 140, 180, 220

Suppose the threshold is:

T = 128

Pixel Value	Comparison	Output
20	20 < 128	0
60	60 < 128	0
100	100 < 128	0
140	140 ≥ 128	1
180	180 ≥ 128	1
220	220 ≥ 128	1

Therefore, the output becomes: 0 0 0 1 1 1

📚 4. Types of Thresholding

1️⃣ Global Thresholding

Uses one threshold value for the entire image.

2️⃣ Local Thresholding

Uses threshold values that can vary across different regions of an image.

3️⃣ Adaptive Thresholding

Automatically calculates a threshold for local neighborhoods.

4️⃣ Otsu's Thresholding

Automatically selects a global threshold by maximizing the separation between two intensity classes.

🌍 5. Global Thresholding

In global thresholding, one threshold value is applied throughout the complete image.

T = Constant

Example:

T = 128

If the object and background have clearly different intensity values, global thresholding can work effectively.

🔍 6. Local Thresholding

In local thresholding, different regions of an image can use different threshold values.

Image

→

Divide into
Regions

→

Calculate
Local T

→

Binary
Image

Local thresholding is useful when illumination is not uniform across the image.

🧠 7. Adaptive Thresholding

Adaptive thresholding calculates the threshold based on the local neighborhood of each pixel.

Two commonly used approaches are:

Mean Adaptive Thresholding

Threshold is calculated using the mean of neighboring pixels.

Gaussian Adaptive Thresholding

Uses a weighted average where nearby pixels receive greater importance.

📊 8. Otsu's Thresholding

Otsu's method is an automatic threshold-selection technique commonly used for separating an image into two classes.

It searches for a threshold that gives strong separation between the foreground and background classes.

Otsu's method is particularly useful when the image histogram has two relatively distinct intensity groups.

Basic Idea

Step 1: Calculate the grayscale histogram.

Step 2: Consider possible threshold values.

Step 3: Divide pixels into two classes.

Step 4: Calculate within-class or between-class variance.

Step 5: Select the threshold providing the desired maximum separation criterion.

📈 9. Histogram and Thresholding

A grayscale histogram represents the frequency of different intensity levels in an image.

Image

→

Histogram

→

Select T

→

Segmented
Image

When foreground and background have different intensity distributions, the histogram can help identify a suitable threshold.

⚫⚪ 10. Binary Image Formation

Thresholding commonly converts a grayscale image into a binary image.

Grayscale Image → Threshold → Binary Image

Black Pixel

Usually represented by intensity 0.

White Pixel

Usually represented by intensity 255.

🧪 11. Interactive Thresholding Demonstration

Enter Pixel Intensity (0–255): Threshold T: 128

Set a pixel value and threshold, then click Apply Threshold.

🧩 12. Thresholding on an Image Matrix

Consider an 8×8 grayscale image represented by pixel intensities. Thresholding converts every value into either foreground or background.

Click New Matrix to generate a grayscale matrix.

🐍 13. Beginner Python Code

The following example demonstrates simple global thresholding using OpenCV.

import cv2 # Read image image = cv2.imread("input.jpg") # Convert to grayscale gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY) # Apply threshold T = 128 ret, binary = cv2.threshold( gray, T, 255, cv2.THRESH_BINARY ) # Display images cv2.imshow("Original", image) cv2.imshow("Binary Image", binary) cv2.waitKey(0) cv2.destroyAllWindows()

Explanation:
cv2.threshold() compares the grayscale pixel values with the threshold value. Pixels satisfying the threshold condition are assigned the maximum value, here 255, while the others become 0.

🐍 14. Beginner Python Code – Otsu Thresholding

import cv2 # Read image image = cv2.imread("input.jpg") # Convert to grayscale gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY) # Otsu thresholding ret, binary = cv2.threshold( gray, 0, 255, cv2.THRESH_BINARY + cv2.THRESH_OTSU ) print("Selected Threshold:", ret) cv2.imshow("Original", image) cv2.imshow("Otsu Binary Image", binary) cv2.waitKey(0) cv2.destroyAllWindows()

Important: With Otsu's method, the threshold is selected automatically rather than manually specifying a fixed threshold such as 128.

🐍 15. Beginner Python Code – Adaptive Thresholding

import cv2 # Read image image = cv2.imread("input.jpg") # Convert to grayscale gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY) # Adaptive threshold binary = cv2.adaptiveThreshold( gray, 255, cv2.ADAPTIVE_THRESH_GAUSSIAN_C, cv2.THRESH_BINARY, 11, 2 ) cv2.imshow("Original", image) cv2.imshow("Adaptive Threshold", binary) cv2.waitKey(0) cv2.destroyAllWindows()

📊 16. Comparison of Thresholding Methods

Method	Threshold	Suitable Situation
Global	One fixed T	Relatively uniform illumination
Local	Region dependent	Different image regions
Adaptive	Calculated locally	Uneven illumination
Otsu	Automatically selected	Images with two dominant intensity classes

🧠 17. Thresholding Algorithm

Step 1: Read the image.

Step 2: Convert the image into grayscale if necessary.

Step 3: Select or calculate a threshold value T.

Step 4: Compare every pixel with T.

Step 5: Assign the required output intensity.

Step 6: Obtain the binary or segmented image.

🌍 18. Applications

📄 Document Processing

Separating text from paper backgrounds.

🔢 OCR

Preparing scanned documents for Optical Character Recognition.

🧬 Medical Images

Isolating regions of interest in some medical images.

🏭 Industrial Inspection

Detecting objects, defects or regions in manufactured products.

🛰️ Satellite Images

Separating selected regions based on intensity information.

🎥 Object Segmentation

Separating foreground objects from suitable backgrounds.

✅ 19. Advantages

1. Simple and easy to implement.

2. Computationally inexpensive compared with many advanced segmentation techniques.

3. Produces a simple binary representation.

4. Useful as a preprocessing step for OCR and object analysis.

5. Automatic methods such as Otsu reduce the need to manually choose T.

⚠️ 20. Limitations

1. Global thresholding may fail when illumination is uneven.

2. Noise can affect the thresholded result.

3. A poor threshold can remove useful object information.

4. Some images contain overlapping foreground and background intensity distributions.

5. Adaptive methods can require additional computation.

🔍 21. Thresholding vs Edge Detection

Feature	Thresholding	Edge Detection
Main Purpose	Separate regions/classes	Find intensity boundaries
Basic Principle	Compare pixel intensity with T	Measure intensity changes
Output	Usually binary regions	Usually edge map
Common Methods	Global, Otsu, Adaptive	Sobel, Prewitt, Canny

🎓 22. Important Examination Points

1. Thresholding is an image segmentation technique.

2. The threshold value is generally represented by T.

3. Global thresholding uses one threshold for the whole image.

4. Adaptive thresholding calculates thresholds locally.

5. Otsu's method automatically selects a threshold using a class-separation criterion.

6. Thresholding is widely used in OCR, document processing, object segmentation and image analysis.

📌 23. Quick Revision Table

Concept	Key Point
Threshold	Value used to separate intensity classes.
Binary Image	Image containing two main intensity levels.
Global Threshold	One threshold for the complete image.
Local Threshold	Threshold depends on an image region.
Adaptive Threshold	Threshold calculated from local neighborhoods.
Otsu	Automatic threshold selection based on class separation.
Application	Segmentation, OCR, inspection and image analysis.

CREATED BY BIJAN KRISHNA PAUL

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