Why is the median filter called 'edge-preserving'?

1. Why does median filter preserve edges?
2. Is Gaussian filter edge preserving?
3. How does the median filter work?
4. How median filtering is used to reduce image noise?

Why does median filter preserve edges?

Since the median value must actually be the value of one of the pixels in the neighborhood, the median filter does not create new unrealistic pixel values when the filter straddles an edge. For this reason the median filter is much better at preserving sharp edges than the mean filter.

Is Gaussian filter edge preserving?

If one method smooths out the large gradient, it is not edge preserving. Such methods include the classical isotropic diffusion filters like Gaussian filter and box filter.

How does the median filter work?

The median filter works by moving through the image pixel by pixel, replacing each value with the median value of neighbouring pixels. The pattern of neighbours is called the "window", which slides, pixel by pixel, over the entire image.

How median filtering is used to reduce image noise?

The median filter is a non-linear digital filtering technique, often used to remove noise from an image or signal. Such noise reduction is a typical pre-processing step to improve the results of later processing (for example, edge detection on an image).