Calculate the output produced if a 3 x 3 median filter were applied to a window, w, centered at coordinate (2, 2).
Understand the Problem
The question asks for the calculation of the output from applying a 3 x 3 median filter to a specified window in the provided 8-bit grayscale image matrix, centered at coordinates (2, 2). This involves identifying the values in the surrounding window, sorting them, and finding the median to provide the output.
Answer
The output is $127$.
Answer for screen readers
The output produced by the 3 x 3 median filter at coordinate (2, 2) is $127$.
Steps to Solve
- Define the window for the median filter
The median filter is a 3 x 3 window centered at coordinates (2, 2). This means we will take the surrounding 3 rows and 3 columns from the matrix:
33 228 236
76 127 107
220 186 3
- Extract values from the window
The values in the 3 x 3 window, as per the coordinates above, are:
33, 228, 236,
76, 127, 107,
220, 186, 3
- Sort the values
Next, we sort these values in ascending order:
3, 33, 76,
107, 127, 186,
220, 228, 236
- Find the median value
For a 3 x 3 window, there are 9 values. The median is the middle value.
Since the sorted list is:
3, 33, 76, 107, 127, 186, 220, 228, 236
The median (5th value) is 127.
The output produced by the 3 x 3 median filter at coordinate (2, 2) is $127$.
More Information
The median filter is commonly used in image processing to reduce noise while preserving edges. The median of a set of values is a robust measure that is less affected by outliers compared to the mean.
Tips
- Selecting the wrong window: Ensure you correctly identify the surrounding values based on the center coordinate.
- Counting mistakes: When finding the median, ensure you are selecting the correct middle value from the sorted list.
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