Explain Segmentation by Region Growing and Region Splitting & Merging.

1. Region Growing

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Definition:

Region Growing is a segmentation technique where the image is divided into meaningful regions by starting with seed points and growing regions by adding neighboring pixels that satisfy similarity criteria (like intensity, color, texture).

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Working Steps:

Let:

• f(x, y) = input image
• S(x, y) = seed array (1 for seed points, 0 elsewhere)
• Q = a predicate (logical condition)

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Algorithm:

1. Initialize Seeds:
   • Identify seed points in S(x, y) based on known values or similarity clusters.
2. Form Predicate Image fQ(x, y)
   • fQ(x, y) = 1 if the pixel at (x, y) satisfies predicate Q (e.g., intensity in a specific range), else 0.
3. Grow Regions:
   • Add all pixels in fQ(x, y) that are 8-connected to each seed.
4. Label Regions:
   • Label all connected components with unique region IDs (e.g., R1, R2…).

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Key Points:

• Connectivity is very important (e.g., 4-connectivity or 8-connectivity).
• Similarity Criteria could be:
  • Pixel intensity range
  • Color similarity
  • Texture match

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Stopping Criteria:

Region growth stops when no neighboring pixels satisfy the similarity condition Q.

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Advantages:

• Simple and intuitive
• Good for detecting connected regions with similar properties

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Disadvantages:

• Sensitive to noise
• Depends heavily on seed selection

2. Region Splitting and Merging

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Definition:

A top-down segmentation technique where the image is first split into subregions, and then merged based on similarity conditions.

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Main Idea:

• Splitting: Divide the image recursively into 4 equal parts (quadtrees).
• Merging: Combine adjacent regions if they satisfy a common predicate Q.

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Steps:

1. Start with the entire image R.
2. Split:
   • If Q(R) = FALSE, divide R into 4 equal quadrants: R1, R2, R3, R4.
   • Continue splitting subregions until all subregions satisfy Q.
3. Merge:
   • After splitting, merge adjacent regions Ri and Rj if:

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Representation:

• This method uses a quadtree structure:
  • Each node has 4 children (subregions)
  • Root = entire image
  • Leaves = smallest regions after splitting

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Conditions:

• Regions must be connected
• Must satisfy predicate Q
• Must be disjoint and cover the entire image

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Advantages:

• Works without predefined seed points
• Useful for images with large uniform areas
• Handles texture segmentation if predicate Q is based on texture

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Disadvantages:

• May over-segment the image
• Predicate selection can be complex

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Example of Predicate Q:

• Q(R) = TRUE if standard deviation of pixel intensities in R < threshold
  (i.e., R is uniform enough to be considered a region)

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Final Output:

A segmented image where each region is:

• Connected
• Uniform according to predicate Q
• Labeled as a separate region