Medianfilter

Medianfilter is a non-linear digital filtering technique used to reduce impulsive noise in images and signals while preserving edges. For each sample, the value is replaced by the median of the samples in a neighborhood, typically a square window in 2D such as 3x3, 5x5, or larger.

The algorithm is simple: collect values in the window, sort them, take the middle value as output. Border handling methods include replicating edge values, reflecting the image, or using padding. In 1D signals, the window is a contiguous set of samples.

Properties: robust to salt-and-pepper noise, preserves edges better than linear filters, but can blur fine texture if the window is large or the noise density is high. It is not optimal for Gaussian noise and can remove small, genuine details. Computational cost is higher than a linear filter, though fast implementations exist using histograms or running medians; real-time processing for small windows is feasible.

Variants and applications: adaptive median filter (AMF) increases the window size where noise is detected; weighted median and rank-order filters provide variations controlling influence of neighboring pixels. Applications include denoising photographs, video frames, medical images, and remote sensing. Limitations include choice of window size, border effects, and reduced performance on structured or textured noise.