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 is asking to calculate the output of a 3x3 range filter applied to a specific section of an 8-bit grayscale image matrix, centered at the coordinates (2, 2). This involves considering the pixel values within the defined window and applying the range filter operation.
Answer
The output of the range filter is $191$.
Answer for screen readers
The output produced by the 3x3 range filter at coordinates (2, 2) is $191$.
Steps to Solve
- Identify the 3x3 pixel window
At coordinate (2, 2), the 3x3 window from the 8-bit grayscale image matrix includes the following values:
[181, 62, 112]
[199, 62, 245]
[248, 114, 253]
- Find the minimum and maximum pixel values in the window
The minimum value is $62$ and the maximum value is $253$.
- Calculate the range
The range can be calculated using the formula: $$ \text{Range} = \text{Max} - \text{Min} $$ Substituting the values: $$ \text{Range} = 253 - 62 $$
- Final calculation
Now calculate the range: $$ \text{Range} = 191 $$
The output produced by the 3x3 range filter at coordinates (2, 2) is $191$.
More Information
The range filter is used to highlight the contrast in pixel values within a neighborhood of pixels. A larger range indicates a higher diversity of pixel intensity values in that window.
Tips
- Confusing the coordinates when selecting the 3x3 window. Always ensure to correctly center the window around the specified coordinates.
- Forgetting to calculate both the maximum and minimum values, and instead only using one of them for the range calculation.
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