Implementing a median filter involves applying a specific process to each pixel in an image to reduce noise while preserving edges. The core method centers around a sliding window that examines pixel values within a local neighborhood.
Understanding the Median Filter
A median filter is a non-linear digital filtering technique often used to remove noise from images or other signals. It is particularly effective at removing "salt-and-pepper" noise, where individual pixels have random, high-contrast values. Unlike averaging filters, which can blur edges, the median filter replaces the center pixel's value with the median of the values in its surrounding neighborhood.
Step-by-Step Implementation Process
Implementing a median filter on an image follows a straightforward process, applying the same logic iteratively across every pixel. Based on the provided steps, here is how it's done:
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Window Selection
Choose a window of a specific size (e.g., 3x3, 5x5) centered around the pixel to be filtered. This window defines the local neighborhood that will be considered for the median calculation. Common sizes are 3x3 or 5x5, but larger windows can be used depending on the noise characteristics and desired smoothing level.
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Collect Pixel Values
Gather all the pixel values located within the selected window. These are the values from the neighboring pixels, including the center pixel itself.
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Sort the Values
Arrange the collected pixel values from the window in numerical sort order (either ascending or descending).
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Choose the Median Value
Identify the median value from the sorted list of pixel values. The median is the middle value in the sorted list. If the window contains an even number of pixels, the median is typically calculated as the average of the two middle values (though some implementations might simply choose one of the two).
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Replace the Center Pixel
The original value of the center pixel of the window is replaced with the calculated median value. This new value represents the filtered output for that specific pixel location.
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Repeat for All Pixels
Slide the window to the next pixel location (typically moving one pixel at a time across the image) and repeat the entire process (Steps 1-5) for every pixel in the image. Edge pixels require special handling; common approaches include padding the image borders or shrinking the window size at the edges.
This iterative process, moving the window and applying the median calculation, results in a new, filtered image where each pixel's value has been determined by the median of its local neighborhood.
Example: 3x3 Window
Let's consider a small 3x3 window of pixel values:
| 10 | 12 | 15 |
|---|---|---|
| 11 | 80 | 14 |
| 13 | 10 | 12 |
The center pixel has a value of 80 (potentially noise).
- Collect values: {10, 12, 15, 11, 80, 14, 13, 10, 12}
- Sort values: {10, 10, 11, 12, 12, 13, 14, 15, 80}
- Choose median: The middle value (5th out of 9) is 12.
- Replace center pixel: The original value 80 is replaced with 12.
The resulting 3x3 section after filtering the center pixel would look like:
| 10 | 12 | 15 |
|---|---|---|
| 11 | 12 | 14 |
| 13 | 10 | 12 |
This process is repeated for every pixel in the image to complete the median filtering operation.
