Kuwahara filter

The Kuwahara filter is a non-linear smoothing filter used in image processing for adaptive noise reduction. Most filters that are used for image smoothing are linear low-pass filters that effectively reduce noise but also blur out the edges. However the Kuwahara filter is able to apply smoothing on the image while preserving the edges. The Kuwahara filter is a non-linear smoothing filter used in image processing for adaptive noise reduction. Most filters that are used for image smoothing are linear low-pass filters that effectively reduce noise but also blur out the edges. However the Kuwahara filter is able to apply smoothing on the image while preserving the edges. Suppose that I ( x , y ) {displaystyle I(x,y)} is a grey scale image and that we take a square window of size 2 a + 1 {displaystyle 2a+1} centered around a point ( x , y ) {displaystyle (x,y)} in the image. This square can be divided into four smaller square regions Q i = 1 ⋯ 4 {displaystyle Q_{i=1cdots 4}} each of which will be where × {displaystyle imes } is the cartesian product. It must be noted that pixels located on the borders between two regions belong to both regions so there is a slight overlap between subregions. The arithmetic mean m i ( x , y ) {displaystyle m_{i}(x,y)} and standard deviation σ i ( x , y ) {displaystyle sigma _{i}(x,y)} of the four regions centered around a pixel (x,y) are calculated and used to determine the value of the central pixel. The output of the Kuwahara filter Φ ( x , y ) {displaystyle Phi (x,y)} for any point ( x , y ) {displaystyle (x,y)} is then given by Φ ( x , y ) = m i ( x , y ) { extstyle Phi (x,y)=m_{i}(x,y)} where i = a r g min j ⁡ σ j ( x , y ) {displaystyle i=operatorname {argmin } _{j}sigma _{j}(x,y)} .