medianifilter

The median filter is a non-linear digital filtering technique used to remove noise from images or other signals. It is particularly effective at removing salt-and-pepper noise, which appears as random black and white pixels. The filter works by sliding a kernel, or window, over the input signal. For each position of the kernel, the median value of the pixels within the kernel is calculated and replaces the center pixel. This process is repeated for all pixels in the image. The size of the kernel, often a 3x3 square, determines the extent of the smoothing. A larger kernel will result in more smoothing but may also blur fine details.

The median filter's advantage lies in its ability to preserve edges better than linear filters like the mean filter, which tend to blur them. This is because the median operation is less sensitive to extreme values (the outliers that constitute the noise). When a pixel with a very high or very low value due to noise is encountered, it is unlikely to be the median of its neighborhood, and thus it will be replaced by a more representative value. The computational cost of a median filter is generally higher than that of a mean filter, especially for larger kernels, as it requires sorting the values within the kernel. Despite this, its effectiveness in noise reduction while preserving image features makes it a popular choice in image processing applications.