Medianfiltrering

Medianfiltrering is a non-linear digital filtering technique used to remove noise from images and other signals. It works by replacing each pixel's value in an image with the median value of the pixels in its surrounding neighborhood. The neighborhood is typically a square or circular window of a defined size, often 3x3 pixels.

The process involves sliding this window across the entire image. For each position of the window, all the pixel values within the window are collected and sorted. The median value, which is the middle value in the sorted list, is then assigned to the center pixel of the window. This operation is repeated for every pixel in the image.

A key advantage of median filtering is its effectiveness in removing salt-and-pepper noise, which appears as random black and white pixels. Unlike linear filters such as the mean filter, which can blur sharp edges in an image, median filtering preserves edges better. This is because the median operation is less sensitive to extreme outlier values.

However, median filtering is computationally more intensive than a simple mean filter, especially for larger window sizes. The choice of window size is crucial; a larger window will remove more noise but can also lead to a loss of fine detail. Despite this, median filtering remains a popular and valuable tool in image processing and signal analysis for its noise reduction capabilities while maintaining image integrity.