Otsu's Thresholding: Adaptive Image Binarization

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Objective

Implementation of Otsu's Method for automatic optimal threshold determination in image binarization. This statistical approach separates foreground and background by maximizing between-class variance, eliminating manual threshold tuning.

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Pipeline Overview

1. Image Acquisition

• Load image using OpenCV
• Accepts both grayscale and color images (converts color to grayscale)
• Fallback dummy image if input not found

2. Histogram Calculation

$$P(i) = \frac{\text{count of pixels with intensity } i}{\text{total number of pixels}}$$

• 256 bins (0-255 intensity levels)
• Normalized to probability distribution

3. Iterative Threshold Evaluation

For each threshold $t$ (0 to 255):

• Split into two classes:
  • $C_1$: pixels $\leq t$
  • $C_2$: pixels $> t$
• Calculate class probabilities:

$$P_1(t) = \sum_{i=0}^t P(i), \quad P_2(t) = \sum_{i=t+1}^{255} P(i)$$

• Compute class means:

$$\mu_1(t) = \frac{1}{P_1} \sum_{i=0}^t i \cdot P(i), \quad \mu_2(t) = \frac{1}{P_2} \sum_{i=t+1}^{255} i \cdot P(i)$$

4. Between-Class Variance

$$\sigma_b^2(t) = P_1(t) \cdot P_2(t) \cdot \left( \mu_1(t) - \mu_2(t) \right)^2$$

• Optimal threshold maximizes $\sigma_b^2$

5. Binarization

• Pixels $> t \rightarrow 255$ (white)
• Pixels $\leq t \rightarrow 0$ (black)

6. Visualization

• Original image
• Histogram with threshold line
• Binarized output

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Foreground/background separation results

Image 1

• Composite output showing original, histogram, and binarized result

Image 2

• Threshold analysis and binarization output

Image 3