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Franciso Zavala
Franciso Zavala

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Nonlinear filters in image processing.

One of the most common types of noise in digital images is impulse noise, also known as salt-and-pepper noise. This type of noise randomly alters certain pixels in the image by setting them to the minimum or maximum possible intensity values (e.g., 0 and 255 in 8-bit images), while the rest of the pixels remain unchanged.

Applying a Gaussian filter in these cases is counterproductive. Convolution with a Gaussian kernel smooths the image through a weighted averaging operation, which affects both noisy and non-noisy pixels. This not only fails to effectively remove the noise, but also introduces widespread blurring in the image

As an alternative, the median filter offers a much more suitable solution. This filter replaces the value of each pixel with the median of the intensity values of its neighbors within a local window (typically square-shaped). By focusing on the central value of the sorted data, the median filter preserves edges and is highly effective at removing outliers such as those introduced by salt-and-pepper noise.
How It Works.

The basic procedure for applying the median filter consists of the following steps:

  1. For each pixel, define a local window of size w × w centered on that pixel.

2.Extract all intensity values within that window.

3.Sort the values.

4.Replace the central pixel value with the median of the sorted list.

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