Calculate the output produced if a 3 x 3 range filter were applied to a window, w, centred at coordinate (2, 2).
Understand the Problem
The question requires us to calculate the output of applying a 3 x 3 range filter to a specific part of an 8-bit greyscale image matrix, centered at the coordinates (2, 2). To solve this, we will identify the relevant 3 x 3 matrix around the center point, apply the range filter, and compute the output value.
Answer
The output produced is $191$.
Answer for screen readers
The output produced is $191$.
Steps to Solve
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Identify the 3 x 3 Matrix
Extract the 3 x 3 matrix centered at (2, 2) from the given greyscale image matrix.
The selected matrix is:
$$ \begin{bmatrix} 231 & 62 & 112 \ 199 & 62 & 245 \ 248 & 114 & 253 \end{bmatrix} $$
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Calculate the Maximum and Minimum Values
Find the maximum and minimum values in the selected 3 x 3 matrix.
- Maximum: $253$
- Minimum: $62$
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Compute the Output Using the Range Filter
Apply the range filter formula which is defined as:
$$ \text{Output} = \text{Max} - \text{Min} $$
Substituting the values:
$$ \text{Output} = 253 - 62 $$
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Final Calculation
Perform the subtraction to find the output value:
$$ \text{Output} = 191 $$
The output produced is $191$.
More Information
Range filters are often used in image processing to reduce noise or highlight features by taking into account the variability (range) of pixel values within a specified window.
Tips
- Mistaking the coordinates and selecting an incorrect 3 x 3 window. Double-check the location of the center point.
- Forgetting to apply the correct formula for the range filter, which focuses on the max and min values.
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