page_title: Kuwahara filter
section_title: The Kuwahara Operator
hierarchical_section_title: Kuwahara filter / The Kuwahara Operator
caption_attribution_description: English: The effect of using a kuwahara filter on an original image(top left) using windows with sides 5,9 and 15 pixels. Bigger windows correspond to more blurry images.
context_page_description: 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.
context_section_description: Suppose that  is a grey scale image and that we take a square window of size  centered around a point  in the image. This square can be divided into four smaller square regions  each of which will be 
  where  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  and standard deviation  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  for any point  is then given by  where .
  This means that the central pixel will take the mean value of the area that is most homogenous. The location of the pixel in relation to an edge plays a great role in determining which region will have the greater standard deviation. If for example the pixel is located on a dark side of an edge it will most probably take the mean value of the dark region. On the other hand, should the pixel be on the lighter side of an edge it will most probably take a light value. On the event that the pixel is located on the edge it will take the value of the more smooth, least textured region. The fact that the filter takes into account the homogeneity of the regions ensures that it will preserve the edges while using the mean creates the blurring effect.
  Similarly to the Median filter the Kuwahara filter uses a sliding window approach to access every pixel in the image. The size of the window is chosen in advance and may vary depending on the desired level of blur in the final image. Bigger windows typically result in the creation of more abstract images whereas small windows produce images that retain their detail. Typically windows are chose to be square with sides that have an odd number of pixels for symmetry. However, there are variations of the Kuwahara filter that use rectangular windows. Additionally, the subregions do not need to overlap or have the same size as long as they cover all of the window.
caption: The effect of using a Kuwahara filter on an original image(top left) using windows with sizes 5,9 and 15 pixels.
exif: {}