Calculate the output produced if a 3 x 3 majority filter were applied centred at coordinates (2, 2).
Understand the Problem
The question is asking to calculate the output of applying a 3x3 majority filter to a given binary image matrix at specific coordinates. This involves determining the value that results from the filter based on the surrounding values in the matrix.
Answer
The output produced is $0$.
Answer for screen readers
The output produced is $0$.
Steps to Solve
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Identify the 3x3 window
To apply the 3x3 majority filter at coordinates (2, 2), we need to extract the surrounding values in a 3x3 matrix centered at this coordinate. The coordinates (2, 2) correspond to the third row and third column in the matrix.The 3x3 window is as follows:
0 0 0 1 0 1 1 0 0 -
Count the values in the window
Next, we count the number of 0s and 1s in this window.- There are five 0s: (0,0), (0,1), (0,2), (1,1), (2,1).
- There are four 1s: (1,0), (1,2), (2,0), (2,2).
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Determine the majority
The majority value is determined by whichever value appears more frequently within the 3x3 window. Here, 0s appear five times and 1s appear four times. -
Output the result
Since 0 is the majority value, that will be the output of the filter for the specified coordinates.
The output produced is $0$.
More Information
In binary images, a majority filter is used to reduce noise by replacing each pixel's value with the most common value in its surrounding area. This is particularly useful in binary images to clean up artifacts.
Tips
- Forgetting to check the boundary conditions, which may lead to accessing indices outside the matrix bounds. Ensure the selected window remains within the matrix limits.
- Miscounting the number of 0s and 1s; it’s important to carefully tally each value in the 3x3 region.
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