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What is a Median Filter?

A median filter replaces each pixel with the median value from a surrounding neighborhood. It suppresses isolated noise while preserving sharp boundaries better than filters that average adjacent values.

How Median Filters work

A median filter is a nonlinear neighborhood operation that ranks nearby sample values and selects the middle one for the output location. Because an extreme sample has little influence on that rank, isolated bright or dark impulses can disappear without averaging across an edge. Window geometry and boundary handling affect the result as much as window size. The operation is typically applied during restoration or mask cleanup before later analysis or encoding.

Key facts

  1. With an odd-sized window, the median is a value observed in the neighborhood, so the filter selects by rank rather than averaging. With an even number of samples, implementations commonly average the two middle values, which can introduce a value absent from the input.
  2. Applying separate medians to red, green, and blue channels can create a color combination absent from the neighborhood. Vector-median methods preserve relationships between components.
  3. A naive implementation sorts every window independently. Sliding histograms or selection algorithms can reduce repeated work, especially for bounded integer sample ranges.

When Median Filters matter

Choose a median filter for salt-and-pepper noise in scans, photographs, or computer-vision inputs. Larger neighborhoods remove more artifacts but can erase fine details and increase processing cost.

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