Calculate the output produced if a 3 x 3 median filter was applied to a window, w, centered at coordinate (2, 2). Then calculate the output produced if a 3 x 3 midpoint filter was... Calculate the output produced if a 3 x 3 median filter was applied to a window, w, centered at coordinate (2, 2). Then calculate the output produced if a 3 x 3 midpoint filter was applied to a window, w, centered at coordinate (2, 2).
Understand the Problem
The question asks to calculate the output of applying a 3x3 filter (median for the first and midpoint for the second) to specific coordinates of an 8-bit grayscale image matrix. The user needs to apply the given formulas correctly centered at the specified coordinate. This involves extracting the relevant pixel values from the matrix for the calculations.
Answer
Median filter output: $133$, Midpoint filter output: $134$.
Answer for screen readers
For the median filter: 133
For the midpoint filter: 134
Steps to Solve
- Extract the Relevant Pixels for the Median Filter To calculate the median for the 3x3 filter centered at (2, 2), we need to extract these pixel values from the matrix:
[ \begin{bmatrix} 177 & 133 & 159 \ 122 & 122 & 157 \ 144 & 90 & 33 \end{bmatrix} ]
So the pixel values are: (177, 133, 159, 122, 122, 157, 144, 90, 33).
- Sort the Pixel Values Next, we sort the extracted pixel values:
[ [33, 90, 122, 122, 133, 144, 159, 177] ]
- Calculate the Median Since there are 9 values, we can find the median by taking the middle value (5th in this case, as $mod(9, 2) = 1$):
[ \text{Median} = 133 ]
- Extract the Relevant Pixels for the Midpoint Filter For the midpoint filter, we again extract the same values from the same 3x3 matrix centered at (2, 2):
[ \begin{bmatrix} 215 & 99 & 16 \ 52 & 120 & 222 \ 117 & 189 & 252 \end{bmatrix} ]
So the pixel values are: (215, 99, 16, 52, 120, 222, 117, 189, 252).
- Calculate the Maximum and Minimum Values Find the maximum and minimum of these values:
[ \text{Max} = 252, \quad \text{Min} = 16 ]
- Calculate the Midpoint Use the midpoint formula:
[ \text{midpoint}(w) = \frac{\text{Max}(w) + \text{Min}(w)}{2} = \frac{252 + 16}{2} = \frac{268}{2} = 134 ]
- Round the Midpoint Value As the last step, round the midpoint value:
[ \text{Rounded Value} = 134 ]
For the median filter: 133
For the midpoint filter: 134
More Information
The median filter helps to reduce noise in the image by replacing each pixel's value with the median of the neighboring pixel values. The midpoint filter averages the maximum and minimum values, providing a smoother result.
Tips
- Forgetting to round: Always remember to round the result for the midpoint filter, as specified.
- Miscounting pixel values: Ensure to extract exactly 9 values for the 3x3 filter, as missing any may lead to incorrect calculations.
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