Comparison Operations in Image Processing

🔍 What Are Comparison Operations?

Comparison operations compare pixel intensities and produce a binary result.

They are the foundation of:

• Thresholding
• Mask generation
• Segmentation
• Rule-based inspection systems

All operations are applied pixel-wise.

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🔢 Basic Comparison Operators

Operator	Meaning
>	Greater than
<	Less than
>=	Greater or equal
<=	Less or equal
==	Equal
!=	Not equal

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🔺 Greater Than ( > )

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

Example

Pixel = 180
Threshold = 150
Result = 255

Usage

• Bright object extraction
• Simple global thresholding

Pros

• Extremely fast
• Deterministic

Cons

• Sensitive to illumination changes

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🔻 Less Than ( < )

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

Example

Pixel = 90
Threshold = 120
Result = 255

Usage

• Dark region detection
• Shadow extraction

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⚖️ Greater or Equal ( >= )

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

Usage

• Inclusive threshold
• Boundary-safe segmentation

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⚖️ Less or Equal ( <= )

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

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🟰 Equal ( == )

Exact value comparison (rare in noisy images).

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

Usage

• Label images
• Encoded mask extraction

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🚫 Not Equal ( != )

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

Usage

• Background removal
• Mask refinement

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🧠 Range Comparison (Between)

\[T_{low} \le I(x,y) \le T_{high}\]

Example

100 ≤ Pixel ≤ 160 → 255

Usage

• Band-pass segmentation
• Color / depth filtering

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⚖️ Comparison vs Other Operations

Type	Input	Output	Typical Use
Arithmetic	Intensity	Intensity	Brightness, blending
Bitwise	Binary	Binary	Mask logic
Comparison	Intensity	Binary	Segmentation

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🎯 Takeaway

Comparison operations are the decision boundary in image processing.

They are:

• Fast
• Deterministic
• Hardware-friendly

Every thresholding method is built on comparison logic.