Thresholding in Image Processing

🎚️ Thresholding Overview

Thresholding converts a grayscale image into a binary image using a decision rule.

It is a fundamental step in:

• Segmentation
• ROI extraction
• Industrial inspection
• Morphology pipelines

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🎯 Fixed Threshold

Definition

A fixed threshold value chosen manually or empirically.

\[I_{out}(x,y) = \begin{cases} 255 & I(x,y) > T \\ 0 & \text{otherwise} \end{cases}\]

Characteristics

• Same threshold for entire image
• No statistics involved

Pros

• Fastest possible
• Fully deterministic

Cons

• Extremely sensitive to illumination
• Requires tuning

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🌍 Adaptive Thresholding

Idea

Threshold value varies locally depending on neighborhood statistics.

Mean Adaptive

\(T(x,y) = \mu_{N(x,y)} - C\)

Gaussian Adaptive

\(T(x,y) = G_{N(x,y)} - C\)

Where:

• local mean \(\mu\)
• Gaussian-weighted mean \(G\)
• bias constant
  \(C\)

Pros

• Handles uneven illumination
• Works well in real scenes

Cons

• Slower than global methods
• Sensitive to window size

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🔁 IsoData Thresholding (Iterative Selection)

Core Idea

Iteratively updates threshold until convergence.

Algorithm

1. Initialize threshold \(T_0\)
2. Split pixels into two classes using \(T_k\)
3. Compute class means \(\mu_0, \mu_1\)
4. Update threshold

\[T_{k+1} = \frac{\mu_0 + \mu_1}{2}\]

1. Repeat until \(T_{k+1} = T_k\)

Characteristics

• Also known as Iterative Intermeans
• Histogram-based

Pros

• Simple and intuitive
• No histogram variance computation

Cons

• Convergence dependent
• Fails on unimodal distributions

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📊 Variance-Based Thresholding (Otsu)

Core Idea

Select threshold maximizing between-class variance.

\[\sigma_b^2(T) = w_0(T) \cdot w_1(T) \cdot \left( \mu_0(T) - \mu_1(T) \right)^2\]

Pros

• Automatic
• Excellent for bimodal histograms

Cons

• Weak for multimodal cases

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🧠 Maximum Entropy Thresholding

Core Idea

Select threshold maximizing total entropy.

\[H(T) = H_0(T) + H_1(T)\]

Entropy definition:

\[H = - \sum_i p(i) \log p(i)\]

Pros

• Strong against histogram shape changes

Cons

• Computationally heavier

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⚖️ Thresholding Method Comparison

Method	Threshold Source	Speed	Robustness
Absolute	Manual	⭐⭐⭐⭐	⭐
IsoData	Iterative mean	⭐⭐⭐	⭐⭐⭐
Otsu	Variance	⭐⭐⭐	⭐⭐⭐
Max Entropy	Information	⭐⭐	⭐⭐⭐⭐
Adaptive	Local stats	⭐⭐	⭐⭐⭐⭐

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🔗 Typical CV Pipeline

Grayscale
   ↓
Threshold Selection
   ↓
Binary Mask
   ↓
Bitwise Logic
   ↓
Morphology

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🧠 Practical Selection Guide

• Stable lighting → Absolute / Otsu
• Histogram unclear → IsoData / Max Entropy
• Uneven illumination → Adaptive
• Real-time constraints → Absolute / Otsu

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🎯 Takeaway

Thresholding is not a single algorithm.

Understanding:

• Fixed decision rules
• Iterative statistics
• Variance and entropy

allows you to build robust and explainable segmentation pipelines 🚀