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 to calculate the output of a 3 x 3 majority filter applied to a specific coordinate in a binary image matrix. This involves analyzing the values around the center coordinate (2, 2) to determine the predominant value within that filter.
Answer
1
Answer for screen readers
The output of the 3 x 3 majority filter at coordinate (2, 2) is 1.
Steps to Solve
- Identify the 3 x 3 filter area
To apply a 3 x 3 majority filter centered at coordinate (2, 2), extract the surrounding values from the binary matrix. The relevant submatrix is:
0 1 0
1 1 0
1 0 1
- Count the values
Next, count the occurrences of each value (0s and 1s) within the extracted 3 x 3 area.
- Count of 0s: 4
- Count of 1s: 5
- Determine the majority value
The majority value is the one that appears more frequently. In this case, since there are 5 ones and 4 zeros:
- Majority value = 1
The output of the 3 x 3 majority filter at coordinate (2, 2) is 1.
More Information
In image processing, a majority filter is used to reduce noise in binary images by replacing a pixel value with the majority value of its neighbors. This application is useful in various fields such as computer vision and image analysis.
Tips
- Overcounting or undercounting the number of 0s or 1s: Ensure to include all nine values in the 3 x 3 grid.
- Misidentifying the majority: Remember, if two values tie, often the convention is to pick the higher value (1).
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