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. It is named after Michiyoshi Kuwahara, Ph.D., who worked at Kyoto and Osaka Sangyo Universities in Japan, developing early medical imaging of dynamic heart muscle in the 1970s and 80s.
The Kuwahara operator
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=1\cdots 4}} each of which will be
Q i ( x , y ) = { [ x , x + a ] × [ y , y + a ] if i = 1 [ x − a , x ] × [ y , y + a ] if i = 2 [ x − a , x ] × [ y − a , y ] if i = 3 [ x , x + a ] × [ y − a , y ] if i = 4 {\displaystyle Q_{i}(x,y)={\begin{cases}\left[x,x+a\right]\times \left[y,y+a\right]&{\mbox{ if }}i=1\\\left[x-a,x\right]\times \left[y,y+a\right]&{\mbox{ if }}i=2\\\left[x-a,x\right]\times \left[y-a,y\right]&{\mbox{ if }}i=3\\\left[x,x+a\right]\times \left[y-a,y\right]&{\mbox{ if }}i=4\\\end{cases}}}
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