Calculate the output produced if a 3 x 3 majority filter were applied centred at coordinate (2, 2).
Understand the Problem
The question is asking us to calculate the output of a 3x3 majority filter applied to a given binary image matrix at a specific coordinate (2, 2). We will analyze the matrix values around this coordinate to determine the majority value (0 or 1).
Answer
0
Answer for screen readers
The output produced by the 3x3 majority filter applied at coordinate (2, 2) is 0.
Steps to Solve
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Identify the 3x3 neighborhood
To apply a 3x3 majority filter centered at the coordinate (2, 2), we need to extract the values in the matrix surrounding this point. The 3x3 neighborhood consists of: [ \begin{bmatrix} 0 & 0 & 0 \ 1 & 0 & 1 \ 0 & 0 & 1 \end{bmatrix} ]
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Count the occurrences of each value
We will count how many 0s and 1s are present in this neighborhood:
- Count of 0s: 5
- Count of 1s: 4
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Determine the majority value
The majority value is the one that appears more than half the time in the 3x3 matrix. Since there are 9 elements in total:
- Majority value is 0, since it appears 5 times which is greater than half of 9 (i.e., 4.5).
The output produced by the 3x3 majority filter applied at coordinate (2, 2) is 0.
More Information
In binary image processing, a majority filter replaces a pixel value with the most common pixel value in its neighborhood. This helps in noise reduction, particularly with binary images.
Tips
- Failing to account for the boundaries of the matrix: Ensure the neighborhood is correctly identified even near the edges.
- Miscounting values: Double-check the counts of 0s and 1s to ensure accuracy in determining the majority.
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